Sorry, I should have defined that. I had originally intended this as a response to another thread about ASI's that would have provided some context for this post. In the end I created a new thread and lost the context.
Problem: in my opinion one of the main problems with ASI's is that too many character's end up with a 20 in their primary Ability and end up looking like clones.
Solution: Basically, to turn ASI's in to extra Point Buy and increase the cost for higher Attribute purchases. As it is right now, using an ASI to increase to a 20 costs the same as increasing to a 12.
Looking at this within that context, it does prevent a lot of high scores. Since you explicitly list costs about 2, I assume you would allow saving points from one ASI to another.
Here are my concerns:
1. Because you are discounting for racial, this is a very strong encouragement to only go with races that give +2 to your primary attack/spell ability score. +1 is possible but rare, and I don't think you'd ever see someone go with a non-favored race since they start off behind and it's even harder to catch up. This limits the race/class combos and takes a lot of options off the table. Mostly ones chosen for flavor to meet a particular concept, only leaving the most optimized.
2. If someone wants to raise a higher ability score, they will have dead levels where they get nothing, having a four level (or more with some multiclassing) delayed payoff. Really, most times you want to raise a score, you'll want to raise a higher one and it will take multiple ASIs.
3. Relating to the dead levels, taking two ASIs to move from an even to an odd, and then another 2 levels to move from an odd to an even means you take 4 ASIs just to get a +1 to a higher ability score. In a 1-20 game, that's all but one. That's a
really slow rate. Perhaps give 4 points of Point Buy each time.
4. The math of the system does not rely on a christmas tree of items, but does have ability score progression up to 20 baked in. I would suggest increasing the proficiency bonus at 4th and 8th each by 1 so the total proficiency range is +2 to +8.