Human brain runs GI and as such if AGI cannot exist then it would mean that the Universe is uncomputable and that our brains run on basically magic we cannot tackle at all. Even in that situation you could get something arbitrarily close to AGI.

>What's your reasoning for thinking ASI might not be able to exist?

I like looking at emergence as phase transitions. Emergence of animal intelligence from lack of it would be a phase transition and emergence of human intelligence from animal intelligence would be another one. It's not guaranteed to work like this but if you look at emergence in other things it seems to work in similar manner. I classify superintelligence as something which would be another transition above us - able to do something that human intelligence fundementally cannot. Idk if there is such thing and as such there is no proof ASI, as I define it, can exist.