And this is not a counter argument against mine. I'm not arguing that these features would not be beneficial for people with a low dex. I'm saying it would be nonsensical for them to exist for low dex people. Low dex people are sloooooow, not evasion monsters.
There are a ton of mechanics that typically mean "agile/dexterous" without being tied to your Dexterity score. Your movement speed, the Cunning Action ability, Uncanny Dodge, Elusive, Ki, the Mobile feat, and similar features. D&D already has ways to be "Agile/Dexterous" without having an amazing Dexterity score. Heck, Barbarians get advantage on DEX saves made against effects that they can see, even though the class is known for brute strength instead of quick movements, and I don't see you complaining about that for being "nonsensical".
And there are different types of agility. Movement speed is different from avoiding fireballs, which is different from being good with a bow, which is different from having nimble fingers. It is not "nonsensical" to have racial/class abilities that increase your affinity with different types of agility, because being good at one doesn't always (or even normally) mean being good or even decent at the other.
I see no reason why it's nonsensical for a Barbarian, which isn't typically known for being dexterous, to have the ability to add an extra 1d4 to Dexterity saving throws that they fail as a reaction, even if they're not good at archery, juggling, or pickpocketing. IMO, it's more nonsensical the other way around, where any "agile" race gets an automatic bonus to their Dexterity score, making them better at a vast swathe of practically unconnected abilities and talents.
So, no, I get your point of "but why can this race be good at this Dexterity-related thing, but not this other", I just think it's plain wrong and nonsense. Not having a High DEX doesn't mean that you can't ever be good/decent with anything related to Dexterity/agility, and thus, Hare Trigger and similar racial features aren't nonsensical and are better design than just giving the race a +2 to X Ability Score or proficiency in X skill.