This is an interesting angle I never considered. Actually, I think there's something I'm missing with the whole point economy of this 2nd test. Feel free to tell me to shove it if I'm not getting a clue, but at this point I'm starting to suspect I'm loony.
According to Shikamaru's estimate, on average, every individual in the swamp spent an ~100CP(?) on proctor seals, which strikes me as a lot of chakra, even spread over 2 days. teams in the know wouldn't have spent any chakra on the first day unless they had a plan to limit seal supply, precluding chakra regen discounts. That's about 15 Mist teams and 4 Leaf teams, for a total of 57 individuals who spent 0CP on the first day. I suppose we could be set to run into teams ~50CP down...
Also, proctors don't have magical access to one huge seal supply, meaning the number of distributors will go down as the exam progresses and pouches empty, making babysitting a proctor a more viable tactic with time. If the seal supply truly ran out or came close to running out, I expect there were some spectacular battles over the last remaining proctors.
The game theoretical incentive seems to be to never spend chakra on seals while preying on teams that have weakened themselves by spending chakra, delaying any interaction as long as possible in a sort of chicken equivalent. Optionally, spend as much chakra as one deems safe right before the end and make a rush for the finish when the chance of interacting with enemies is lowest. Before then, the only incentive to spend chakra on seals is if one thinks one has done a less than average job of taking seals from other teams, forcing one to make up the deficit. Otherwise, spending chakra on seals lowers the chances of winning in a fight and gives victorious opponents more points, for no gain.
To sum up, I'd divide the exam into 2 conceptual stages. 1. If you have a ridiculous amount of chakra like Naruto or expect to perform middlingly, deliberately decrease the available seal supply to lower variance/prevent anyone else from winning. 2. Prey on teams who cave to getting seals until the last moment, where based on performance, spend chakra on seals last minute or finish the exam. In the absence of Naruto, I'd expect the vast majority of seals to remain unclaimed.