But I also fail catastrophically once a reasoning problem exceeds modest complexity.
I also fail catastrophically when trying to push nails through walls by I expect my hammer to do better.
I have one hammer and I expect it to work on every nail and screw. If it's not a general hammer, what good is it now?
You don't need a "general hammer" - they are old fashioned - you need a "general-purpose tool-building factory factory factory":
https://www.danstroot.com/posts/2018-10-03-hammer-factories