Interesting idea, but it sounds like you're advocating for a change in existing competitions, and I don't expect them to be open to this, especially as it seems that it would make assessment an order of magnitude more subjective and complicated.

Perhaps launch your own online competition and see how it goes?

EDIT: Thinking some more about this, I think it could be even more interesting as a two-round competition. I'm imagining that in round 1, you give all participants an example/theme that they have to stick to, and they have to discover and prove a conjecture about it, under a relatively short time limit. Then, in round 2, all participants are given the conjectures from all other players (perhaps even in a "prove or disprove" form), and players then get points both for proving each other's conjectures and for having proved one in round 1 that is particularly difficult for others. In this way, you don't have to rely on subjective assessment.