The fact that there is an "Animus" makes any sort of story in the AC series pretty fucking stupid. See the ending to AC2, oh lord that was a complete fucking mess.
I disagree completely.
The Animus is one of the few reasons I actually like the AC franchise. It's definitely not because I like Ezio. If you just made a game that was AC2 -- the GTA:Renaissance Italy that it was -- and you took out the ridiculous plot twist ending and the reason for the conflict (racing templars to get the golden apple) I probably would have stopped playing halfway through.
Hell, the ending to AC2 had me dreaming of what sort of epicness the next AC game would bring... and instead of any of it, we got Brotherhood, where it was more of AC2 plus multiplayer. And then they continued to beat that cash cow with Revelations. When they finally said "oh, people are getting tired of this shit, let's do something new", we got AC3, which is still, as far as I can tell, more of the same in a different setting.
If you want to know what I was hoping for after AC2, I've put the gist of it in spoilers here:
I thought that sounded a hell of a lot more interesting and fun... but then again, I'm usually in the minority, liking games that people hate and hating games that the masses adore, so it probably would have been a financial failure for Ubisoft.