[joe_the_user]

I don't think this is just matter of just unprovable theorems being unreachable.

There isn't an equivalent "no conceptual framework is 'best' for all mathematical inquiries" theorem. Such a claim probably can't be proven. But as you say, that doesn't keep it from being true.

Still, Godel's theorem on the cutting down of proofs via assume unprovable claims is worth considering. http://en.wikipedia.org/wiki/G%C3%B6del%27s_speed-up_theorem