I just miss the fanfare/theme, I don't think it makes the game significantly worse.

What makes Final Fantasy 'Final Fantasy'? The makers. Nothing else.
The design team probably looks absolutely nothing like the one that worked on the original FF. If you consider FF to be a legacy series (something that will go on for generations, with new teams picking up after old ones) then the only thing that ties it together is the continuity of stuff like chocobos, common musical elements, ect...
And yes, some stuff has been added after the series progresses. As a matter of fact, I don't have any objection to new traditions being established as of now. What I do have a problem is that the old traditions (the only things that really mark a game as a 'final fantasy') are seen as things to be put in out of convenience. If that is the logic then they should make the game the best they can, and decide after if they should call it an FF title.
When I play a numbered FF title I like to feel like I am playing the thirteenth installment in the franchise, not some JRPG they decided to slap the FF label on to sell more copies.

That wasn't very coherent except the last sentence, so I'll try to do better after you rip it apart.