Since I am very well acquainted with the current situation regarding the faucets, your reasoning is partly correct. There are those bad faucet owners who have just that modus operandi to set a very high threshold for withdrawing funds, so that most users bring some profit to the owner, and never get anything in return. But most faucets have been using something called a microwallets for years, so when you claim on faucet payment is instant to microwallet like off-chain transaction. This is also solved problem of dust transaction.
I may be wrong, but somehow I don't see that LN is something that could be successfully applied to faucets at this point.