My question is, there is a market for that? Thanks
And be careful you don't fall into the "unlimited hosting for a fixed price" trap.
Didn't there used to be a 3rd party Dropbox app that published a folder as a website? (Not the "Public" folder which, I suppose, is another option for some people).
You might be able to do it by generating the gzipped versions yourself and putting CloudFront in front of you site, but I haven't tried.
You could definitely do it with Cloud Flare. If you don't care about ancient browsers and bots that don't understand gzip, you could pretty easily just have gzip-only versions of everything.
I wouldn't expect much more from a $1/month service, but I would expect better service.