Another perspective on stealth for your table

To make matters far worse. First, go to youtube and search for "Simons Selective Attention Test" or watch this if the link acutally works then come back. 

Now, when interpreting the hide action and having the invisible action while hidden for players, I disagree that a hidden player who enters line of sight is automatically found, because that interpretation doesn't quite capture what a very stealthy expert at hiding does.  In this case, given the right distractions, a player could well walk in plain sight and simply not be noticed, especially in a distracting situation like combat, which the above video mimics (the opponents are tracking the actions of the people trying to lop their head off, not the gorilla).  Similiarly, a stealthy player hiding in a crowd and so forth would be in the plain video, but unnnoticed. Even in far less distracting circumstances, a player could create distrtions, or wait for the creatures they're hiding from to turn their attention elsewhere as they move through the space in plain view.  Finally, there are the inevitable examples, say from movies, where the person hiding is simply in a place the other creature does not think to look, say, up in a tree. For additional examples, watch any video of a magician explaining a trick, many of which rely on distraction to hide things in plain sight.  Rewatching the magic trick once you know where to look for the ball makes you wonder how you missed it the first time.  

This is to say, staying hidden isn't a matter of staying out of sight, but rather staying unnoticed, quite often by staying out of the selective attention of the creature you're staying hidden from, because this is the way perception and attention work in brains. 

For my table, if a rogue with stealth expertise is sneaking around, once hidden, I find it entirely plausible that they can break cover and enter plain sight while remaining unnoticed because the expert stealther knows how to take advantage of how attention works to be within the line of sight, but unnoticed. A stealthy hidden player in combat of course comes into view when attacking, but I rule they still have advantage, because they know how to time their strike for the exact moment when the target's attention is somewhere else.  
Similarly, this gets much harder when the target is actively aware of them and looking for them (taking the search action), which is why the odds of success go down when the stealth is opposed. (and if they're not taking a "search" action in combat, its because they're doing something else, like trying to hit someone else and therefore clearly distracted)

So, this language of "you have the invisible condition while hidden" does not mean "you have the invisible condition while behind three quarters cover or heavily obscured" as some interpret it, but rather "you have invisible condition until something breaks your hidden condition"

I'd be curious what your thoughts are about this real world/narrative interpretation of continuing to be hidden after coming into the  line of sight.

I don't think this really adds anything new to the discussion, sorry. Stuff like this has been brought up before, multiple times. The counter-argument is that this rationale for the chosen interpretation bleeds over into situations where it really doesn't make sense... like a rogue breaking cover to walk down a 100' well-lit hallway with no objects, and with two guards posted at the other end whose only job is to make sure they see people coming down the hallway.

I don't think a hidden creature  Heavily Obscured or behind Three-Quarters Cover or Total Cover is automatically found, it may or may not be successfully perceived, just like the gorilla in this video, which some people see while others don't.

But if there was no players passing the basketball to conceal the gorilla, it would be easily perceived.

"While hidden" it is reasonable for a DM to impose Disadvantage onto active or passive Perception checks situationally (distractions, etc).  But if you are not hiding then you do not enjoy any of the benefits of being hidden.

The point is that the interpretation that you’re seen the instant you break cover is pretty silly, because for one thing it negates any ability to gain advantage on any attack while hidden, because as soon as you move to see a target from a hidden position, their panopticon awareness sees you and you’re not hidden and lose the invisible condition.  

that interpretation is the one I am reacting to.   Of course, this also makes seeing the hidden character considerably more situational.