Why not? It works perfectly as long as you do it right, and is fully in line with all of the server’s limitations.
Web hosting. As in every file stored on your account should be directly for the site. Hosting video and audio files on your account itself (without embedding from a different source) is specifically against the TOS that you agreed to when you signed up. If what you want is to let your users download the files, you can do that by hosting them on cloud storage (such as Google Drive) and sharing the download link on your site.
The premium plans at iFastNet have the same content rules and still don’t want you to host audio or video files directly. Many hosting companies have similar restrictions on shared web hosting.
If you really want to make an audio streaming site where the content is hosted on the same server, you’ll be better off getting a VPS and doing everything manually. You’d have much more freedom that way.
You wouldn’t have to delete your site either way. You can just make a backup of it and host it elsewhere.