Let me add that I'd be perfectly fine with this
Originally Posted by Scribe
Within my own alternative character generation method, I dont even have the ASI completely tied to race. I have it broken down as.

Lineage +1 ASI (depending on Lineage, so no you cannot put your Halfling +1 in Str)
Background + 1 ASI (each Background provides 2 or more options for an Attribute to be increased per my own assumptions)
Class + 1 ASI (each Class provides an ASI increase to 1 of 3 Attributes.

No Attribute may be increased by more than 2.

That way, you get to have your Halfling with +2/+1 however you like, but only because your whole character builds up to that combination.
Your race gets you a small bonus to a stat.
Then your background gets you a bonus (my halfling was experimented similar to Captain America, gaining it +1 Str)
Then your class (representing training)

This is a good balance of preserving difference between races but allowing flexibility of backgrounds/classes/roleplaying/etc.