What about something like this.
Race and culture grant +1 each, and class and archetype grant an other +1 each. For example, a High (+1 Intelligence) Elf (+1 Dexterity) Arcane Trickster (+1 Intelligence) Rogue (+1 Dexterity), builds a character with +2 Intelligence and +2 Dexterity.
Along with +2 and +2, it is also possible to build a character with +2 and two +1s, or even four +1s. (Depending on an even or odd base, both the +2 and the +1 can be useful.)
Some players can appreciate how this method encourages a race-class combo that is suggestive, thematic, and useful. Other players can appreciate how this method allows freeform combinations that are viable.
Mostly I am happy with the above method. My only difficulty is the lack of ‘superhuman’ flavor. What I love about 5e is how the Human ability is +1 or +0, where the Nonhuman races can feel superhuman because of a +2. Super strong, super smart, super charming, etcetera. At the same time, a Human can if desirable, spend the feat to boost the score to total +2, so somewhere there is an individual within the Human population who is just as able as one of these superhuman races. Which also feels right.