that's sort of how reversathon setups work, too, though, and the way it tends to work is that a few people get *all* their requests picked up, most people get one or two picked up, and then there are a few that I have to scramble for because the requester is asking for fandoms nobody knows, or unpopular pairings, or just asking for things that don't stand out.
I mean, there could be a rule that you can't nab a second one of somebody's requests until everybody's had one filled, but that seems more likely to just stall out the claiming process than encourage people.