In my honest, unbiased opinion, it's all up to where one started with the franchise as to where its "mojo" stemmed from. For me, that was in the PS1 era. I can't discredit FF7 for actually putting Final Fantasy in the mainstream market. But it's always going to be different for other people-- "nostalgia goggles" be damned. (and boy I sure am with the others here-- I hate that insulting old umbrella term. It looks like nothing more than a blatant verbal attack to me.)
I dislike the more recent games not because "oh no it's new and different and I don't like change wah wah look at me I'm whining" but because I deeply, profusely dislike Nomura and Tabata's writing. They're into things that I'm definitely not a fan of; Urban fantasy, for one. Their characters barely appeal to me save for some background noise, and their stories meander off into directions that make me want to spit. If Hiroyuki Ito were put back on board, I'd probably return to loving the franchise as a whole. But for now, my interests are divided.
I love Nomura's art, though. Beautiful character designs. He should have just stuck to that. Although, I will say that his work on FFVIII was an exception for me. That one was, after all, my gateway game. So who knows-- maybe even he can change my mind. But it would take a lot of effort on his part. Tabata... not so much. He has never once directed a single game that I enjoyed.
I prefer to think of it in this light: Way back in Andre Norton's later life, she launched a massive project called "Witch World", which enlisted young and new authors to submit short stories set within its canon world, following some very loose rules. Some of these young authors were one-hit wonders. Others-- well, they wrote something, that's for sure- but their writing just was not good enough to get them the right publicity. And then there are those that moved on to be great authors, like C.J. Cherryh or Mercedes Lackey. Among these stalwart authors, there were (and are) still some not-so-great ones, but they somehow still get their work's worth of fame. They must be appealing to some kind of audience, but it's not the kind that's looking for solid, sensible storytelling. Same thing goes for the likes of EL James and Stephenie Mayer. If we apply that to videogames (and it's not that hard to)- those in charge of the writing and direction of the title should be noted and recognized for their past credentials.
Going back to Final Fantasy & Nomura and Tabata, their track records remain static for me. They, as writers and directors, have taken the franchise in their direction, and it will never change unless they change their style OR another director is put in charge in their place. These guys are to be held accountable for everything because they're the ones that give the ok for battle mechanics, UI designs, the whole nine yards. In the end, they do appeal to a large audience, otherwise they wouldn't be able to stay afloat as directors. We can also apply that to FFIX, Hironobu Sakaguchi, and Hiroyuki Ito-- Ito and Sakaguchi were the ones that made IX possible, and for some, that's not a combination that worked well. For me it's a dream team, the likes of which we may never see again. Those are just a few of many names that have become famous off their work. And as some directors and writers grow older, their sensibilities mature, and they might take to concepts they hadn't before. Some even fall from grace. We can observe examples of this distortion of direction elsewhere, in the Tales series, in Elder Scrolls, in Thief and Tomb Raider and so, SO many other things. For better or worse. And fan incentive can't exactly influence that.
But... I probably said too much now. TL;DR version: It's not the times that I care about, but who's in charge and what THEY, as people, are doing. So it gives me hope, knowing that 1) FF never has the same director/writers for long and 2) people are always changing-- game devs included.