I absolutely love old-school FF. I would be beyond thrilled if we got a new mainline FF game in the mold of one of the SNES games, but with a modern AAA budget and tech. But FF reinvents itself constantly, and having been on forums for 25+ years at this point, I've seen complaints like this for literally every FF since VII.
I recall people back in the day who were worried that FFVII "wasn't FF" because being a top-down RPG was core to FF's identity. This seems quaint now, but it was a genuine fear people had once FF went to PlayStation.
For FFVIII, people were upset that the game didn't use traditional equipment, and that enemies scaled with the party, and that you didn't get Gil from killing monsters. I even remember people being upset that the dialogue boxes were gray and not blue.
FFX got huge amounts of hate for abandoning the previously-traditional scaled world map you could walk around on, and for its linearity in general.
The complaint about XII at the time was that it "played itself" and was "an offline MMO." People were afraid that the game would barely be interactive. Even Penny Arcade made fun of it:
I suspect if you went far enough back, you'd find people freaking out about that newfangled ATB that they were putting in FFIV, and how "real" RPG's were supposed to give you unlimited time to make your choices.
This is what FF does. It changes, potentially more than any other series of its stature. And every single time, some people love those changes, and some people feel left behind by them. Both are legitimate perspectives (again, I wish they'd go back to ATB and traditional job systems, personally!), but no one should be surprised by this anymore.
As far as whether or not FFXVI will be a strategic game, that's hard to say without playing it. Action games have their own elements of strategy that are hard to translate to turn-based games, such as spacing, positioning, and timing. And I'd be hard-pressed at this point to say that older FF games are particularly strategic, as far as RPG's go: apply buffs, use spells the enemy is elementally weak to/mash Attack, rinse, repeat. We've all done that a million times and I don't think anyone is breaking their brain playing FF in the same way they would playing, I don't know, a good CCG.
Additionally, there's nothing inherently "more" strategic about picking options from a menu while a game is paused vs. executing them in real time; the question is,
what are the options that are available to you as a player? I wouldn't be at all surprised to find that FFXVI has buffs, debuffs, elemental weaknesses, etc. on par with prior FF games, and we already know that it has accessories and gear. If XVI ultimately offers players the same options older FF games does, does it matter what inputs you use to perform them?
Finally, the obligatory "no one here has played the game yet." I remember thinking VIII and XIII looked amazing from the trailers, and they both ended up being among my least-favorite FF games. I thought XIV looked bad until I played it, and now I love it. We'll see what happens at launch, but I doubt things will be as cut-and-dry as some people think.