Often an applicant they turn down will get funding elsewhere and experience notable success or failure.

The problem is, this generally isn't the case. If a proposal passes, then your standing on the board is guerenteed to change, whereas if a proposal fails, then standings will only be adjusted if some other group decides to implement a similar measure. Humans are notoriously risk-averse, and we tend to fear losing things that we already have more than we value gaining new things. Consequently, I'd be concerned that such a set up might incentivise voting down unorthodox proposals that other organizations are unlikely to implement. If it such a proposal passes, then you are will definitely either gain or loose standing, whereas if it's rejected, your standing will likely remain unchanged.