IMHO, there is nothing wrong with free hosting. A faucet script can be run on any barebone system really, it should be light weight.
However, there’s no such thing as a free lunch and something has to give.
A paid plan will usually be better in every way. I personally run my faucets on InMotion hosting.
I don’t know if they are the best, I’m sure they aren’t the cheapest...
But!!!
They do have good speed, good uptime, unlimited bandwidth, unlimited storage, unlimited size on db, free ssl included, very competitive pricing and great customer support. So, for overall package, I find them hard to beat. Others might be better in certain areas but usually the others fall short in one way or another instead.
Send me a pm if you’re interested, I’ll get you a ref link.

P.S. Any downtime for my faucets have usually been due to third party fail and outside my control. So, rarely if ever has it been the hosting.

Edit. I dunno about Bitcoin? Only paid for my plan once and after that things have been humming along nicely.