You're right by definition - TileMill doesn't serve maps. Right now it generates them, and TileStream serves generated maps. It's extremely fast and stable, but inherently limiting.
That's not to say this won't change in the future :)
That's not to say this won't change in the future :)
There is a TileStream Hosting service that has integration with a CDN & DropBox, stats, etc. It uses the open version and just adds glue code to services.
Thank you.