A faucet website does not require too much spce and bandwidth to run so shared hosting is enough .
I am running my faucet website in less than $1 per month cost .
Thats true. a faucet does not really need big hosting packages and bandwidth do host faucet sites. a simple and built in faucet like faucetbox faucet can be easily setup on a free webhosting service. and I think faucets should host in free services. because faucet's traffic are almost direct from faucet lists and the forum and premium domain and hosting could be good for something which really need big work like SEO Etc.
and free domain also can be listed in Search engine.
Hostinger got some free domains, but be careful i heard from 3 people that they just removed the free hosting packages (no reason given).
And for me being into faucets quite some time, a free domain faucet is always ignored by me.