Reading those four bullet points together makes me think you're not only after elimination of ability scores but elimination of classes as well.
I can see how you'd reach that conclusion, but no, I would never eliminate classes. They do constrain your options, but they offer major benefits to make up for it. Ability scores (IMO) do not.
The class system allows the designers to custom-tailor a suite of mechanics to fit a particular concept; ensure those mechanics work in harmony; balance them against other classes across a range of power levels; and present the entire package as a single choice to be made at chargen. This is incredibly helpful to the novice gamer, who can just pick an option off the menu and be done. And for the veteran, these customized suites greatly extend the replay value of the game. Bored with playing wizards? Try a warlock, or a fighter, or a rogue--it's a whole different way to D&D*.
This kind of thing, where you get a packet of mechanics bundled together in service to a concept, is one of D&D's strongest features. But I want the packets to be as independent as possible, allowing them to be mixed and matched. So you pick your class, and your race, and some skills; and ideally any combination of these things should result in an effective character. That ideal may be impossible to achieve in practice (and feats are a whole other can of worms), but it's possible to get tolerably close.
Ability scores introduce a ton of unnecessary dependencies. Class, skills, and (until TCoE) race all hook into ability scores, and you get punished mechanically for choosing combinations that don't fit. On top of that, ability scores themselves have concepts attached to them, telling you that your character is strong or weak, smart or dumb--so that's another factor pushing and pulling at your stat picks, depending on how much you care about it.
And they add substantially to the complexity of the game,
and the concepts attached to them are sloppy and ill-defined (is Wisdom perceptiveness or willpower? and why the hell would you describe either one as "wisdom?"),
and they've got the silly split between "bonus" and "score" where you almost always care about the bonus but once in a while you want the score instead. They're just a mess all around and D&D would be better off without them.
Of course, that's never going to happen. Ability scores are too bound up in D&D tradition, trying to excise them would provoke the mother of all backlashes. WotC will never get rid of them entirely. But every time they sever one of those dependencies, I cheer them on.
And that's why I wholeheartedly favor "no racial stat mods," or failing that, the floating-mod system in Tasha's. It's one more dependency severed.
*This is somewhat undercut in 5E by the existence of the "full caster" and "multi-attack martial" archetypes, which between them encompass 10 out of 13 classes. Switching from wizard to sorcerer, or fighter to ranger, does not provide nearly as much mechanical variety. On balance, I think this is a weakness, but if the designers had had to create twelve fully unique classes to launch 5E, they'd still be working on the PHB today.