With the new Monster/Races book out, I was excited to check out the options. I ended up focused on the Lizardfolk and realized it, imo, is badly designed due to possessing 2 (functionally) mutually exclusive racial abilities. Their bite attack uses strength for hit and damage, as it is an unarmed strike (and they have another special bite attack, so this problem actually affects 3 of their racial features). Their natural armor uses dexterity. I think it's one thing if a racial ability is mutually exclusive with or rendered moot by a class ability, but racial abilities should all work together and be viable together, imo.

We all know that raising both str and dex to high scores is generally not done. You'll mostly invest points in only one or the other, or even neither. Of course, nothing is stopping a low str character from making the bite attack, anyway, but it feels like wasted action economy, which feels bad. 

This book started introducing racial spell features that allow you to choose Wis/Int/Cha as the spellcasting stat. This was an awesome improvement to game design. I wish they extended this design philosophy to racial attacks as well, allowing you to choose str or dex for "natural" unarmed strikes. I think it'd be easy enough to get your DM to approve, but I'd still like to see official implementation. 

Any other opinions or observations on this issue/book or a similar subject? Thanks for your consideration!

Theses Lizardfolk features are exactly as they were in the Legacy version in Volo's.  If you absolutely want to maximize your racial features over anything else you can optimize in a character, I guess you need to focus on two stats.  The natural armor uses the same rules for AC as regular armor without a dex cap that a 13 AC usually imposes.  I think this is actually balanced design versus your ideal, which I feel is asking too much if you look at the context of AC in the rest of the rules.  

Besides STR = AC is unheard of, maybe CON if we're talking toughness and can draw from Barbarian formula, then you'd have a triad of stats to maintain.

I don’t see them as mutually exclusive. That would be something more like having sunlight sensitivity and not having dark vision. Then you can’t see no matter where you are. 
Having powers that key off two different ability scores is simply asking you to choose which, if either, you want your character to be better at doing. Forcing a player to make a meaningful choice, instead of letting them just put all their effort in one place and be good at everything, is a sign of good game design, imo.

Getting an AC of 13+Dex is great at low levels for classes like Barbarian, Sorcerer, or Monk.  Being limited to Strength for your natural weapon attacks is more problematic but matches with the natural weapons of other races and most of the time if you're a class that relies on melee combat you're going to have a better weapon anyway- something that's at least a D8, possibly higher.

I fail to appreciate the problem with the Lizardfolk's bite attack; it's still 1d4, and even with a negative Strength modifier you'll still do potentially do more damage with that than an the certainty of failure with an Unarmed Strike. Though I do think that with more emphasis on choosing a stat such as Dexterity, that could be done, especially with something that would likely come so naturally to creatures with Natural Weapons.

I disagree that these things should complement one another, if anything the variety means more nice-to-have's. I dislike how three of the four Minotaur traits are all related to their Horns attack, thus requiring greater Strength to make the mechanical choices worth it (and are they when as 6thLyranGuard above me mentions, you'll likely have a better melee weapon)?

The question is balance.

Take the Wood Elf (with their racial ASIs) as an example. All their abilities and ASIs towards Dex and Wis make them great Rangers. If their ASIs were towards Int and Cha, then we'd have a problem. Their abilities are good individually, but they'd never be good at any class because their abilities don't harmonise. If you went Ranger, they wouldn't get very useful ASI, if you went Wizard their abilities would be marginally useful, etc.

The question is, if they're mutual exclusive (or effectively so), are you given two good choices to choose from or are they two mediocre ones that would make a good race if they were compatible, but aren't and so you end up with a mediocre one?

I've not really played with a martial class so I can't really tell you which. Natural weapons always seem a bit underpowered for me, so I don't know.

Is paladin a bad design because it doesn't use the same stat for attacking and spellcasting? Reliance on different stats is a balancing mechanism, and there are a lot of mechanics all through the game that discourage reliance on a single stat above all else (there are some exceptions like many rogues or hexblades to a degree, but that's what they are - exceptions to the rule).

Not every racial feature needs to be - or even is intended to be - leveraged to the max for a given character. Also, these are just established things. AC relies on DEX, even in unusual cases like mage armor, and unarmed strikes rely on STR with the sole exception of monks. So breaking that pattern is going to have effects beyond the race. Now if you want to complain about the old lizardfolk design that has features reliant on STR and DEX but its racial bonuses were CON and WIS, I think that's a legitimate gripe. But the new design is better in that regard.

I will say that Hungry Jaws does push you pretty hard into a STR build in order to make use of it. That doesn't really jibe with the new stat-agnostic design approach, but it's also a really fun flavorful ability and I'm glad they didn't kill it completely. But while it's easy to say that they could just allow natural weapons to use DEX, I don't think you appreciate what the consequences of that change would be. It would affect monk, which is currently the only way to get that kind of thing, it would affect the overall relative utility of STR and DEX in general, which is already in a sad state and doesn't need the scales tipped even further in favor of DEX. It would just not be a good decision.

Lizardfolk do not need strength.  They need Dex.   Yes, your bite uses your strength.  So what?  The damage is minimal (1d6) and the Temp hitpoints  are only a couple times a day.  It's a good thing, not a necessary like AC which is used all the time. You do not need to maximize every possible aspect of your build, especially at low levels.

The way to play a lizardfolk is to keep your Strength low (12 is nice) and get yourself a Belt of Giant Strength at some point in the future.  Your Dex you max out for the AC.  Your magical belt makes your Bite still usable but you do not depend on it for the main build.

When not wearing armor, your armor class is primarily determined by your Dexterity. When making an unarmed strike, the attack and damage are modified by your Strength. That's not a description of Lizardfolk, that's a description of everyone prior to adding class features that modify those things.