Mostly a good post, but there's no contradiction with 3e or 5e racial ability bonuses and the races themselves.
Where 3e messed up was not in the racial bonuses, but in keeping the racial penalties. Those penalties created more of a class pigeonhole than bonuses ever did. Especially in a system where the bonuses and improvements were baked into the math.
5e did not do that. There is neither contradiction, nor any sort of pigeonholing going on. Anyone who feels otherwise is psyching themselves into believing something that the math doesn't bear out.
With a +2 5e is easy. With +3 it's very easy. With +4 it's incredibly easy. And with +5 it's a virtual cakewalk. Unless the DM increases the difficulty anyway.
In 5e, where the human average is +1, a +0 is an ability score "penalty", narratively.
Mechanically, within the context of 5e design of bounded accuracy, each bonus increase becomes exponentially more powerful. In many contexts, including proficiency bonus and typically a magic bonus, a +5 ability bonus is virtually an autowin, followed up by a routine advantage die, just in case.
The head start by a race ability score improvement is an extreme incentive for a race to pick only certain classes in 5e. The absence of one is a punishment, both narratively being less than a human and mechanically losing out on a feat in order to catch up mathematically.
Meanwhile, the ability score improvement itself as a mechanic is a blunt instrument at best, and often handicap the playability of the tropes of a race.
For many reasons, the race ability score improvement is a bad gaming design. It fails to accomplish what it intends to do, namely mechanically quantify the tropes of a race. Also it causes more serious problems ethically because of its reallife racist origins, that are at best old fashioned, and at worst objectionable in todays sensibilities.