At first, I thought that this wouldn't really be used, however something like this could be interesting. I'm thinking of it as an actually used and decent replacement to rating threads, which already exists.
For this to be cool, I think it would need to be a button for the community to press, in a much more obvious place in the OP than the current rating thing. After a certain amount of votes to promote the thread, it would get bumped up with the tag, maybe to a separate section below stickys. Art threads with well-made art would get boosted, funny wibbles threads would get boosted, good discussion and off-topic threads would get boosted, etc. Clan discussion and recruitment boards, as well as other boards where this would be less than useful, would have this disabled.
I think the feature would get used, but we'd need to make sure that it doesn't get abused. Making sure only 1 user and 1 ip could vote, etc. (this should also be applied to polls tbh)
As for the shiai prize, I think it would be interesting to award contributing members of the community with something besides Tori Legend, something smaller and not as difficult to achieve. Maybe, if it's shown that promoted threads work and are something that's actively used, you could get a shiai reward after having a certain amount of promoted threads. Maybe there would be a community vote to give people a prize. That's something to discuss elsewhere from this thread, though.
People who have a lot of promoted threads would have some more references when applying for moderator/squad positions, too. It would certainly be a good thing to have, if it were made to work well and the community weren't to abuse it.