I don't think this is obviously correct.
Three things:
1) Many actions we think of as "intelligence" are just short-cuts based on heuristics.
2) While there's probably an argument that problem solving is selected for it's not clear to me how far this goes at all. There's little evidence that smarter people end up in more powerful positions for example. Seems like there is perhaps there is a cut-off beyond which intelligence is just a side effect of the problem solving ability that is useful.
3) Perhaps humans individually aren't (very?) intelligent and it is only a society of humans that are.
(also perhaps human GI? Nothing artificial about it.)
> no idea how large the search space is for finding AGI, so applying something like Bayes theorem (which is basically my argument) tells you more about my priors than reality.
There are plenty of imaginable forms of intelligence that are often ignored during these conversations. One in common use is "an intelligent footballer" which applies to sport for someone who can read a game well. There are other, non-human examples too (Dolphins, crows, parrots etc).
And then in the world of speculative fiction there's a range of different types of intelligence. Vernor Vinge wrote about intelligences which had motivations that people couldn't comprehend (and Vinge is generally credited with the concept of the singularity). More recently Peter Watt's Blindside contemplates the separation of intelligence and sentience.
Basically I don't think your expression of Bayes' theorem had nearly enough possibilities in it.