Why? Why do you need something to be defined? You're willing to rewrite what you don't like, but aren't willing to choose between, or combine, two or four possibilities. I honestly don't get this.
I'm not sure what's not to get. A toolkit is versatile, sure, but it's also work by default. Worse than that, it's about as flavorful as instant ramen with half a spice packet. The DMs (and possibly players depending on how much authorial control the DM is asserting over the setting they're running) have to add all the spice themselves, and when you're preparing dozens of dishes or more, that adds up.
Super defined races(and monsters) may not always be what you want, but they're always
something, and you're just as free to edit to suit your tastes as you are with a toolkit, but if you just need something to spark the imagination, defined is going to do that far better than not, even if it sparks your imagination in how you
don't like the definition.
And I don't see that as logical. What's logical is to have racial traits. Halflings get Nimble, which means all halflings, whether they're very strong, very smart, or very dexterous, are Nimble; and Lightfoot halflings are also Stealthy. Forcing all halflings to put +2 in Dex and have Nimble and maybe Stealthy is not only redundant, but boring as well.
It's
very logical unless you just don't want there to be differences between races at all. Even a slower than average adult cheetah will be faster than a hippo after all. And taking away ability score bonuses and other features won't make them
less boring. If anything, I'd want to go the other direction and add more defining features given the considerably greater number of playable races that WotC has introduced. But the point of racial ASI isn't to make - in this particular example - all halflings dexterous. It's to make halflings, on average, more dexterous than other races that don't have the same ASI. It's perfectly possible to have a clumsy halfling, a halfling that never skips leg day or a halfling mastermind. But the +2 Dex means that there are fewer clumsy halflings than dwarves, and fewer halfling Schwarzeneggers than orcs.
If a player wants their character to be one of the exceptions, they'll need to spend the points(or choose the appropriate array, or hope for a good roll, or whatever) to get there. Or their gaming group can decide they don't like the assigned ASI and just allow it to be put wherever. That's still a choice a group can make regardless of what's written. But taking away the defined ASI in text is limiting the options for those who prefer defined races.
You just say "I want this," but never why. Why is it so important that a halfling have Nimble, possibly have Stealthy, and also must have +2 Dex but never +2 Wis or +2 Cha?
The reason is as simple as can be: because it supports the base premise of wanting greater definition to distinguish each race from each other.
Personally speaking, my big complaint is that D&D wants to bake its cake once and eat it several times over. If it were up to me, I'd ditch the idea of having an "official" campaign setting represented in the big three books at all. Make the PHB and MM pure classic fantasy, stereotypes on full display. Orcs are evil raiders, elves are stuck up tree huggers, all that crap. The PHB should give new players a clear and simple "this is what you're getting with this race." The MM should allow an inexperienced DM to thumb to an page, get an instant idea of what a particular monster is and how it would fit into an encounter or campaign. Simple, hyper defined, and hitting exactly the notes you'd expect of a classic fantasy setting.
Then I'd take each published campaign setting, and put out an "Ecologies and Societies" book that largely forgoes the mechanical crunch except to point out variants or where they differ for that specific setting, instead focusing more on behavior, regions settled, societal roles, etc. Where the MM might paint orcs in a way befitting a black and white antagonistic role, the E&S would instead go into detail about different tribes (if they're even organized as tribes in a particular setting), the customs they might have, the relationships they have with their neighbors, etc. Going into that kind of setting specific detail isn't really possible in the baseline books without making those books worthless for all other settings, and making the baseline books generic without publishing anything else is just as bad, forcing DMs and players alike to obtain books from older editions(which newer players and DMs obviously won't do) just to get a good feel for what makes them different in each setting.