BTC faucet is a bad idea, tx cost and amount of time to get withdrawal is insane. But, altcoins exists.

Lets take Clams for example:

As a faucet owner imagine you have 1500 Clams that are staking on justdice. They generate 1 Clam everyday. You take that 1 Clam and redistribute it to faucet users based on their claim. Your 1500 Clams are still staking. Then you use ad income to increase your Clams. Lets say you earned 100000 satoshis from ads. You use that satoshis and buy more Clams and now you have 1502 Clams. They generate 1.002 Clams every day. As you use ads income to increase your staking balance, faucet payouts grow. Users of faucet are paid quickly, they see proof and come back...

This is a theory, mathematicians please contribute.