I feel like one of the best things D&D could do is get rid of ability bonuses entirely. It's been heading that way since the beginning. At first non-human/elf/dwarf/hobbit characters weren't even playable, then they were added to AD&D with some major drawbacks like min/max ability scores. In 3e, that got changed to bonuses and penalties. In 4e and 5e that was reduced to just bonuses plus extra abilities.
One approach that would still give the same feel is requiring ability score minimums for certain races, like dwarves that must have a minimum of CON 9, or orcs requiring STR 9. That would limit dump stats for point buy and determine where certain scores are assigned for rolled stats without limiting which races and classes could possibly be viable combinations. When certain races get +2 to one ability or another, it pretty well pigeon-holes them into certain classes for point-buy (less so for random rolls). The great thing about minimums (especially low minimums) is that it prioritizes certain combinations without making them strictly necessary. So, even under point-buy your githyanki cleric or gnome fighter are viable combinations, even if they have a little more intelligence or charisma than you might prefer if you were to min/max.
That is a nice way to handle it. Personally I think it would be enough if you just gave every character a +1 to a single other attribute of your choice in addition to the normal bonuses. That way no matter what race you pick you'll always at least be able to hit 16 in your primary combat stat.
So my Dragonborn druid would still get a +2 in STR he doesn't need and a +1 in CHA that isn't valuable, but as long as he can get 16 WIS or CON (depending on Circle) he'd be just as viable as any race that got a +1 or +2 in WIS. The +2 strength and +1 charisma would just feel like a nice bonus at that point rather than a waste of points. You'd still have optimal race/class combos but the difference between them and non-optimal combos would be much more marginal and likely weighted more toward the actually fun racial features rather than attribute bonuses.
Plus it'd represent your character's individuality and personal training and experience that isn't necessarily shared by every member of your race.
