Except that a Mac mini can't actually do the stuff an Apple TV does. It doesn't support AirPlay from iOS devices*. It doesn't have a simple, full screen "channel" list of things to start watching. You can't do much to control it using only the simple apple remote; you actually have to keep a bluetooth mouse/trackpad around or use something like HippoRemote on iOS to operate it.
No, a mini is not an Apple TV replacement. Not at all. If you actually want an Apple TV for the things that an Apple TV does, a mini is quite inferior.
I don't have an Apple TV, but I do have a mini. I originally bought it to act in lieu of an Apple TV (as well as being an alway-on file server). Now it's just sitting in a corner acting as the file server, disconnected from the TV, because it cannot in fact perform the Apple TV's role.
This isn't to say that a Mac mini isn't a fine computer. It is, I just don't care about that; I work on an iMac. My mini serves a critical role I need so no regrets getting it; it'd just have been nice if I got an Apple TV out of it too.
* Not out of the box at least. There do appear to be 3rd party AirPlay servers for OSX now. I haven't tried any since I gave up on using my mini as an Apply TV long ago, before these applications existed.
Maybe that's the key. And that's just not an option for me. The router is quite far from the TV, and houses wired for ethernet have become a thing of the past with aways-improving wifi technology.