CubicsRube
Hero
For my preferences I prefer one of two ways.@CubicsRube ,
After a discussion the other day, here is what our table decided on for our games from this point forward:
Standard array is 14, 13, 12, 11, 10, 9.
Point-buy is 21 points, 14 max (costs 6, not 7)
Rolling: you roll d6 three times, and use the middle result, add 8. Repeat 5 times for your six scores.
Then you have a +2 ASI and +1 ASI to place where you want, but a score cannot exceed 15 (so you can't add the +2 ASI to the 14).
You gain a +1 ASI every other level, starting at level 2 (then 4, 6, 8, etc.).
This caps total bonus to +4 at level 1 (not as low as the +3 in your design), but allows the PC to grow as you suggest via ability scores.
Finally, you still get the regular ASI/feats at levels 4, 8, etc. and can use them normally: so either a quick bump to an ability score +2 or a feat.
1) Use the old school method of higher starting stats but then rarely if ever increasing these, or
2) have a low array with increases and growth built into the system.
For me, 5e sits between these two poles. Your method is a little higher than where I think I'd go for my personal tastes, but much more in line with the second concept above.