a 15 Strength is not its +2 modifier
The +2 modifier is not an effect of the strength score. God.
The +2 modifier is just another way of representing one aspect of what a 15 strength score
is.
Yes; in plain English, we say that the score gives the bonus, but, mechanically, that's not what happens: you don't cast your strength to get the score; you don't ask your strength to provide the score. The score and its bonus are just different representations of the same thing.
To suggest otherwise is to claim, for example, that a function causes its curve.
Similarly, no one burns an offering of a feat-slot to a feat-spirit to receive a feat-effect in return.
As part of level-gain, a character has the option of changing his aspects. The term 'feat' just refers to and codifies this change.
So, by taking Improved Initiative, it becomes an aspect of the character that he has a +4 to his initiative. He doesn't cast Improved Initiative on himself to receive the effect of the bonus.
No; he changes his abilities as a result of gaining in level. The changes are an effect of leveling up, and we call these changes feats.
The mistake, the huge and maddening mistake, is to regard the
feats themselves as the source of the change they represent.
It's like saying that the word 'aging' causes people to grow old. Or that numbers cause things to add up.
Normally, this doesn't make any bit of difference: the reification of the feat has no consequences.
But in this case mistaking the representation for the thing itself confuses things terribly and results in absurdity. Pretending that feats generously divest themselves of their benefits at the petition of the characters is fine for ordinary language, but to try to apply that as a description of how the pieces of the game fit together is pure superstition.