Nothing wrong with setting up your own web page, in fact, if you manage a software project you should do that. The simplicity of GitHub is in the code management features. AFAIK, they don't provide website functionality, and what they do provide doesn't need to be perverted for that purpose.
Now, it's perfectly reasonable to use version control separately for built projects (it's not unusual for entire websites to be inside VCS), but not in a subdirectory of the source code tree, and you certainly shouldn't make your users dick around with the VCS ever, ever, ever.
If the site is removing direct download then it's no longer suitable for use and should be abandoned. Sites like SourceForge still do direct download without issue, and as bxs demonstrated, so does GitHub.