If you can’t get ssh access, and you’re not dealing with a service that specifically hosts discourse, then it’s not going to happen. The technical issues make this a hard limitation.
The issue with people who would like to use their current shared webhosting for discourse seems to come down to just a few things.
They aren’t savvy to the ability to host a subdomain of your main site elsewhere, with the result being the end user has the same experience.
They don’t have the tech know how to install discourse via ssh on their own vps/dedi.
The solution I’ve been offering people is to provide clean installs on a relatively inexpensive vps. If they would like to consolidate their projects onto one server, then I offer a service to enable you to host your php/html5 (wordpress blogs, for instance) sites from the same vps.
My latest install included multiple discourse instances working alongside wordpress blogs. I setup the system and ran through the commands necessary to setup additional sites by doing the first wordpress install via skype share. I work with the customer to get them where then need to be, independent of their current skill level.
To wrap up, shared hosting option would be nice, but is not currently available through nearly all major providers. There is hosting specifically for discourse, via this main site, and discoursehosting.com. If you’re looking for a cheaper route, and a way to run wordpress and/or php/html5 sites alongside discourse, I can setup a vps for your needs.