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.
Interesting thought; however I'm not sure what else could motivate them.. Do you have anything particular in mind (even if just pure speculation)?
Here's relevant post. IMO their motivation is either data collection or disrupt Bitcoin development. Claiming "free" token/coin usually require your email address and accessing their website (which means they obtain your browser fingerprint). On extreme case, they might ask for KYC verification.
Please don't give TNBTC to people who are just hoovering it up to paid by defi scams based on it.
Real testing just needs tiny amount, the people who "need" large amounts are selling it. (technically trading it for defi testnet defi tokens which they expect to get converted into real value once that scams they are participating in go live).
This abusive and anti-social behaviour has made it hard for people to get testnet for actual bitcoin testing because they've drained all the faucets and conned the people that have historically given it out out of theirs.
It's also forcing bitcoin development to abandon testnet for testing.