I know that at the end of the day, it’s my decision as the DM what to do with my players, but I wanted to see some opinions on the matter.

To be blunt, I’m tired of the “But does MY character see it?” / “Can MY character try that?” as the third, fourth, fifth player says when no one passes a Perception check or a Nature check (yes, they do exist).

I’m thinking of just implementing using Passives after the first legitimate check, so my players don’t just form a line and try to see the trap/enemy/treasure/etc etc.

Is that unfair to the other players? I know every scenario can’t be covered by a blanket rule concerning this, but for simplicity’s sake, what do you think about using Passives after the first check fails?

For stuff like perception or intelligence-based skills, usually I'd allow everyone in the party to make the attempt.  For some specific circumstances I might say that you require proficiency, like making an Arcana check to decipher a code used only by a secret group of wizards.  I definitely wouldn't go with one person being allowed to make a perception check and sticking everyone else to whatever their passive perception score is.

If it's something I feel all members of the party might notice like an ambush while they are traveling, then I have everybody roll. When I describe the situation I make it clear that some folks see the thing and others are oblivious. 

If they are searching a building, only the PCs in the immediate area of XX can roll for any Perception or Investigation on XX. For the dog pilers, I make it clear that they are not there so can't make a roll.

I am in agreement with 6thLyranGuard that sometimes you only get to roll if you have proficiency in the certain skill. If you don't have proficiency in Medicine, you do not know anything about diseases or first aid so can't roll.

Begin and end with the fiction.

When players ask to make a roll, ask what their characters are doing. If what the characters are doing is vaguely possible in the gameworld then allow it, and then determine success failure. If the character has no real chance of success, don't ask for a roll, just say "no". If the beefy barbarian just failed to break the lock using strength, the puny wizard doesn't even get to roll.

Do it the other way as well. If the character has no real chance of success, don't ask for a roll, just say "yes". If the beefy barbarian tries to break a door, then the door breaks. No need for a roll, they are a beefcake, breaking doors is what they do.

Keep time in mind

If player A has their character do something that is going to take a while, ask the other players what their characters are doing, and do this before resolving character A's thing. If the other players say "nothing" then that is exactly what their characters do for the next 10 minutes (or however long). If character A fails and player B wants to try, make sure to ask them "that is going to take another 10 minutes, are you OK with that?" If they answer "can't I do that while A searches" the answer "we already determined that you didn't do that."

Enforce time

Make additional wandering trap monster rolls. Count down spell durations. Make the time count so that if players choose to have five characters all do a long activity one after another then they pay the consequences.

I really despise successive dice rolls. Let's say it takes 20 seconds to resolve. You have a party of six, and character A rolls, and fails. Character B wants to check, so spends 10 seconds persuading me let them roll, then they take their 20 seconds to resolve, and so forth. Assuming each person from start to finish takes 30 seconds to resolve (10 seconds to get my permission, 20 seconds to actually roll etc), that's three minutes of rolling. Yawn.

If it's a perception check or similar where they all react at the same time, then get everyone to roll as a group, not sequentially. They can pick one person to do a representative roll, or just roll individually and accept the consequences.

If they want to lock pick, make sure there's a consequence for failure or repeated attempts. Perhaps more guards will arrive or the person they're chasing has an extra attempt to escape. Just make it meaningful - or you might as well abolish dice and say that they succeed.

they can all roll at the same time, to save time. You can even do a group check and average it....but I've only seen that used for stealth.

To counter this problem, what I do is allow anybody who wants to roll to do so. If everybody else only wants to roll until after the first guy rolls low, then I'll let them know they can but the DC is going to be higher. (Regardless of if there's actually anything there or not.) And if they roll low and someone else wants to check it goes even higher. 

If everybody wants to roll at the same time, then it becomes a group check. I add up the number of successes and fails (with Nat 1s counting as two fails and Nat 20s counting as two successes) and that determines if the group sees it or not. 

For Perception I usually just have all eligible members of the party roll simultaneously, then grant everyone the benefit of the highest roll provided they can communicate. Party members doing something else that requires their attention aren't eligible to also make Perception checks at my table; you gotta prioritize your focus.

For knowledge rolls, I tend not to let PCs spontaneously acquire information from nothing; if they have a relevant proficiency, or if their background reasonably could have led them to encounter the knowledge they need, I'll let them roll for it. Otherwise no dice.

For physical rolls I borrow a mechanic a few other RPGs use called Pushing the Roll. Any PC can retry any physical check, but each time they do the check gets harder, and the consequences get more dire. Failed to bust down that door? Sure, you can try again, but... Do you think anybody heard that? If there's anyone nearby they'll definitely be listening closely now. That kind of thing.

Quote from Greenstone_Walker >>

Begin and end with the fiction.

When players ask to make a roll, ask what their characters are doing. If what the characters are doing is vaguely possible in the gameworld then allow it, and then determine success failure. If the character has no real chance of success, don't ask for a roll, just say "no". If the beefy barbarian just failed to break the lock using strength, the puny wizard doesn't even get to roll.

Do it the other way as well. If the character has no real chance of success, don't ask for a roll, just say "yes". If the beefy barbarian tries to break a door, then the door breaks. No need for a roll, they are a beefcake, breaking doors is what they do.

Keep time in mind

If player A has their character do something that is going to take a while, ask the other players what their characters are doing, and do this before resolving character A's thing. If the other players say "nothing" then that is exactly what their characters do for the next 10 minutes (or however long). If character A fails and player B wants to try, make sure to ask them "that is going to take another 10 minutes, are you OK with that?" If they answer "can't I do that while A searches" the answer "we already determined that you didn't do that."

Enforce time

Make additional wandering trap monster rolls. Count down spell durations. Make the time count so that if players choose to have five characters all do a long activity one after another then they pay the consequences.

 Bingo.  Thank you Greenstone Walker.  OP, get into the habit of enforcing “turns” in your games- that is to say 10 min increments of time where players engage in an activity of some sort, then are allowed to make the check by the end of it.  If they all want to spend the turn doing that instead of anything else they  could be doing with the turn then fine, but that’s the trade off they don’t get to do anything else with the turn, now roll for a random encounter (trap, wandering monster, cave-in, NPC etc) every 3 or so turns. 

If it’s something like noticing an ambush or that the ledge might not hold their weight or a trap, I would look at the player’s highest passive perception.

If a player is looking for a secret door and you are using Investigation then I would allow someone who had proficiency in that skill use the help action to give advantage. But I wouldn’t allow players to go one after the other. I would go so far as if the first player failed, retcon and give advantage (allow a second roll) if another player spoke up after the fact (just after the first players roll) and they they wanted to Help action and had proficiency. 

Edit: Basically, if it isn’t something they are actively attempting (searching for traps, for example) then use the passive scores. If they are actively doing something (decoding runes on a statue) only if they have the relevant skill proficiencies and if more than one character has prof then group them together for one roll with advantage (Help action). Or if you do want a roll to notice something, again group them together and have them all roll at the same time “Everyone make a Perception check” and see how it plays out. 

Matt Colville has a video on "Skill Dogpiling" that addresses this concern pretty well. Worth a watch. 

The reason people all decide to attempt a check is because outside of combat there's often no meaningful cost to the attempt, so there's no reason they shouldn't. In general your choices are

• Allow everyone to make the check.
• Allow everyone to make the check, but give penalties because multiple people interfere with one another.
• Make the check one where failure locks out future attempts. For example, if trying to disarm a trap and failing causes the trap to go off, retries are moot.
• Assign a cost to the check (or a failed check). In the simplest case this just a (meaningful) quantity of time, but things like damage or fatigue also work.

The other thing is that "X rolled badly on perception, so I should try" is metagaming. Best solution is to require everyone to declare before anyone rolls.