They must have an incentive. I can't really believe that paying the hosting of a faucet website plus the mining costs are less than the ad revenue, but they must have a profit somehow, otherwise they wouldn't mine. That profit may not be translated into money.

There is "testnet 4" called signet that is used now, because of blockstorms and other testnet issues. Getting large amount of signet coins is easier than testnet coins, so testing in signet should be easier. Also, the only reason why someone would need huge amounts of that coins is just for paying minimum transaction fees. But assuming zero satoshi outputs and one satoshi per byte fees, that means every 0.01 tBTC is enough to create 1 MB of test transactions. That means 2.5 tBTC is enough to send 250 MB of test transactions. But then, does someone really need to put 250 MB on-chain? Or maybe that amount of data could be lowered by using Lightning Network inside testnet?