Ideas are cheap and proof is expensive. It’s impossible to give all ideas equal consideration. You have to apply a filter, it’s inevitable. The question is just what filter you apply.
Ramanujan was missed by at least one maths professor. Also, there are mathematical proofs such as that of Fermat's last theorem, or the claimed proof of the abc conjecture by Shinichi Mochizuki for which verification is very difficult.
I'll agree that the costs don't come close to replicating work by LIGO or CERN.
There's a difference between a flawed proof (e.g. Wiles's original proof of FLT which was found to contain a gap) and outright crankery, though. There are more mathematical cranks than most people would think, and their arguments usually fall apart rather easily.