On freebitco.in it takes me around 10 seconds to claim their faucet, but the main reason to go there several times per day is not claiming the minimum reward, which is $0.002 in BTC, but the potential opportunity to win $20 or even $200.
Regarding to the OP's question, if, apart from claiming 5 cents in BTC, there were some kind of a lottery in which there would be 0.01% chance of winning, say, $100, that wouldn't add much to the budget of the project, but the project itself would be much more successful, because it would be easier to promote it.