Xeviat
Dungeon Mistress, she/her
You certainly could, but why? What would be the purpose of the change? As I see it, you are possibly gaining a +1 or maybe +2 bonus to your total modifier by the end of the game compared to if you begin at 16 (+3) and don't bump it.
FWIW we use a modifier proficiency progression from +2 to +8, capping abilities at +4 for a while. We did it because we felt proficiency should count for more in the game. The difference between a level 1 pc (+2) and level 18 (+8) of +6 feels better than the RAW difference of only +4.
So, why do you want this? From your OP I just don't see a big reason for it? Can you elaborate more please? Maybe some concrete examples?
I thought I went into it in my OP.
The reasons I thought of this change were:
1) To diversify character builds (now you could have a smart fighter, or a charming rogue, not everyone would have their highest stat determined by their class).
2) To remove trap choices (related to 1, but you aren't punished for, say, playing a tiefling rogue and now you're starting with a lower Dex).
3) To make the game easier to balance.
4) To make less race/class combos sub optimal.
The new variable lineage ability scores works towards a few of these, but you're still limited in your stat choice by your class.