More than anything else, that just speaks of the inability of the D&D mechanical language to describe things that aren't humans.
I don't know that it is unable to do so, but rarely that it typically has been considered too much of an edge case to spend actual rules on, leaving it up to the DM to rule on the fly if, for example, a PC thief polymorphed into an ape wants to try picking a lock with a set of thieves tools.
It's a mostly-reasonable abstraction to link manual dexterity with agility when you're talking about mostly-athletic mostly-human adventurers - they types of adventurers who have great manual dexterity are also the types who are likely to have great agility. It doesn't make as much sense to link manual dexterity with agility when you're talking about a cat or ape.
Or an elderly woman, who might have better manual dexterity than the adventurers, but also have difficulty walking. But yes, each of the six standard ability scores bundles together concepts that are not identical and sometimes have questionable relation to each other. You could easily break each ability score into three different concepts and have a system with 18 ability scores. But then, this wouldn't be perfectly realistic either, plenty of characteristics like speed and agility are actually not independent. Agility is not solely dependent on your strength to weight ratio, but is limited by it. Strength is not solely dependent on mass, but is limited by it, and certain applications of strength - punching power for example - are additive with mass, while effective punching power is also limited by technique which is again limited by agility.
You have to balance realism with playability, and recognize further that the more complicated your system is, the harder it is to play test, and the more likely it is that it in some way breaks when stressed. Simple systems may never give truly 'correct' answers, but by being abstract they tend to give usable answers and are easier to balance.
And in the actual context of this discussion, they avoid purity for reality aesthetics that force you into awkward conversations about the combat ability of human females prior to the gender liberating invention of the firearm, or the societal importance of military hierarchies prior to the same invention.
Abstraction is your friend in a lot of ways. Don't knock it too much. It only seems like it has a big disadvantage on describing things compared to reification when you have actually tried hard to use reification. I have tried going the other way before - look up GULLIVER for GURPS - and in the context of GURPS, it's theoretically easy to separate out a gibbon or caracal's agility from its ability to hold and manipulate objects. But the trouble is, to accurately represent animals requires massive stat blocks that rarely have to do with anything important enough the game that you'd actually roll the dice to represent it. And if it's not important enough to test with fortune, then it's really not important enough to care about mechanically.
Still, if you really care about these body plan issues and sense of realism, my advice would be to compile a list of Disadvantages (anti-Feats) which describe body plan limitations - blind, lame, no-manipulative digits, quadruped, serpentine body, one-handed, one-eyed, deaf, no depth perception, limited fine motor control, and so on and so forth. In addition to helping you describe animals in those rare cases where it matters, many of these Disadvantages can help you describe a critical hit system if you are into that sort of thing. Virtually any wound can be described abstractly (there is that word again) as a combination of ability score damage and/or disadvantage infliction.