The problem is, you don't have to program the bit that says "now make yourself more intelligent." You only have to program the bit that says "here's how to make a new copy of yourself, and here's how to prove it shares your goals without running out of math."

And the bit that says "Try things until something works, then figure out why it worked." AKA modeling.

The AI isn't actually an intelligence optimizer. But it notes that when it takes certain actions, it is better able to model the world, which in turn allows it to make more paperclips (or whatever). So it'll take those actions more often.