Like what? Almost every Final Fantasy title introduced a new gameplay style. If you've played more than 3 of them you'd see that they're all quite different from each other regarding mechanics. Only the superficial things like monster design and iconic figures like Cid have gone unchanged.
FF is known for changing the gameplay elements more or less. When they change something, that's as "Final Fantasy" as it can get.
Not really. Outside of those they simply introduce a different character management or battle system as their draw point (FFV/IX's ability system, FFVI's Relics, FFVII's Materia System, FFVIII's junction system, FFX/X-2's battle system, FFXII's Gambit/License system, FFXIII's battle system as major examples) which very rarely if at all ever traversed to another title, the only major example I can think of FFX's sphere grid which was used in various forms in X-2, XII and XIII.
There's still common elements shared amongst those systems that have been carried over from game to game; in fact, from probably the 1st game to the 9th, your mode of interaction with the game and its world remained largely unchanged, as did many elements of the games themselves. It wasn't until the PS2 era that they started making really radical changes to how the games work. FFX saw the loss of the whole concept of a world map, taking the concept of the airship and an element of exploration with it. FFXII did away with the whole notion of random battles and the turn-based ATB setup, as well as taking away a degree of control from the player by having the other two characters controlled by the (customizable) AI. FFXIII, as I understand it, was extremely linear; however, since I haven't played it, I can't say for certain if it's killed off anything.
This is why I think they need to consider abandoning the Final Fantasy franchise. It seems like everyone has in their mind a preconceived idea of what a Final Fantasy title should be and should have, and it seems like for each new title, people aren't finding what they're expecting because what they expect wasn't what they got.
I think Square would have an easier time delivering titles without the preconceived notions of what a game should and shouldn't be before it hits the drawing board, especially since some fans can't even agree with each other on what makes a FF game beyond basic elements like Chocobos and Cid.
I don't think abandoning the franchise is really the answer. I'd say they need to go back and replay the older games in the series and figure out what made them more fun than the newer entries, and how they could improve upon them.