so checking it through to understand why, and check it's really true, actually is worth it.

Yes, but that's not quite the same thing. Like an NP-complete problem, there's a world of difference between doing the minimal work to verify the accuracy of a provided candidate solution and doing the exhaustive search required to find a solution from a standing start. Of course I check my insights after I have them, but that's not the thing I'm talking about.

I think your last paragraph is coming close to it, though.