"Can I host my own mobile website?"
Nope - though this isn't a bad thing:
A big part of what MoFuse does behind the scenes is that we're constantly updating and optimizing our platform so mobile sites hosted with us maintain full compatibility with the more than 5,200 (and counting!) mobile devices on the market globally. To accomplish this, we maintain a proprietary database that identifies individual mobile device and browser characteristics to ensure that the viewer gets the best possible experience for their device.
Granted, building and maintaining these sorts of databases might be a hobby for you, which is great (we don't judge). Spending more money to spend more money, probably isn't. Were we to offer a self-hosted solution, we would be unable to offer such a solution at price points that we find acceptable.
tl;dr: No, because part the service that we offer is adopting mobile-related headaches so you don't have to, and, such a solution would cost end-users more.