You're looking at it completely wrong. First of all what you described was divergence, not convergence. Convergence would be a Mac mini with an Apple TV UI (or an iOS emulator, if Apple TV gains iOS) replacing Front Row, but still running full OSX. Essentially you'd have macs with an Apple TV mode that was easily accessible. I could see something like that coming in 10.7. What I could not see happening is the Mac Mini being split (diverging) into two computing lines, with one of them solely dedicated to media playback, running iOS on hardware that can't even support it (natively). All for what amounts to a minimal discount from a full fledged computing platform. That seems like an even worse strategy than the current Apple TV.
Lets look at this another way. The 16GB iPad costs $499 and is capable of playing back anything in the iTunes store. Take out some of the largest and most expensive components (the screen and the battery) and add a TV UI and you have a tiny, capable, and cheap set top box that absolutely sips power (it can run off USB power).
A revamped Apple TV will spawn from iPhone/iPad hardware if it's running iOS. There is no need for any of the Mac Mini hardware to show up in a new Apple TV, and if iPad hardware is used, there would be a ton of empty space in a case with the same footprint as mac mini or current apple TV. The Mini isn't supplementing Apple TV in that form factor, it is replacing it. Apple TV is likely destined for much bigger things (by becoming smaller and cheaper).
I think we're both going in the same direction with our predictions, just from different starting points. I'm coming from top down, you from the bottom up.
In think we're both at the idea that aTV will be something like the iPad but as a set-top box. I don't think there's anything wrong with either of our arguements. The point i was trying to make was that the new mac mini, seems to be incorporating more and more aspects of the aTV. And, the aTV now is sort-of being shelfed at it's current state.
what this says to me is that they are either
1. getting ready for a complete re-vamp of the aTV, or...
2. getting ready to dump the aTV and create a new class of iDevice like an iHome/iTV/iWhathaveyou, or...
3. going to eventually created a sub-set of the Mac Mini as a HTPC
All these ideas get to a point where, im not even sure Apple knows where its going, we have some kind of home server or media center.