I have to agree with those above, I think it might help if they make true sequels rather than unplanned cash-ins with the sole intent of reusing assets. It's not about sequels themselves being bad; people love sequels. Sequels to big games often sell better than their predecessors, and the excitement surrounding the announcement of big name sequels is always huge.
The problem is almost certainly that XIII-2 and Lightning Returns were slapdash, sloppy efforts that were in no way up to the quality of XIII. XIII-2 doesn't have the same polish even at a glance, and LR is even more guilty of this. It all seems oddly phoned-in compared to the content that it sprung from. Of course, I understand why from SE's perspective. They needed the cash, and they had all of these resources they'd spent years upon years developing for use in just one game. It seems like a natural choice, but in hindsight it's foolishly short-sighted.
Squirrel Emperor raises probably the most interesting point to me, which is how unfaithful the sequels were to Final Fantasy XIII. If you had given me a synopsis of XIII and XIII-2, I wouldn't have said they were in any way related. I was not XIII's biggest fan, but even I was less than pleased by the drastic change in direction and focus to more ridiculous and far less cohesive story elements like time-travel and Valhalla. To a lesser extent, I could say the same about X's sequel. It kept the world cohesive, but the tone and direction was so different that it might as well have been its own game. There seems to be an issue with keeping the sequels consistent with and faithful to the titles that they sprung from. Understandable, I suppose, because I think both titles were supposed to be standalone games. Sequels came after the fact.
Going forward I'd actually hate to see SE abandon the sequel idea. Some of my favorite games have had grand stories told over several titles, and I think that Final Fantasy could naturally and easily fit this mold. I believe that setting out with sequels in mind would really help, in order to create a more consistent multi-part story. If that's not possible for any reason, then at least make sure that the sequels are of the same or better quality in technical terms. All the best sequels do what their predecessors did bigger and better, with exciting additions. And, even if the sequel is not planned, try to deliver on something true to what the first title delivered on. No out of left field plot points like time travel or adding a cutesy animal sidekick.
It is my hope that this is more or less what XV is doing. It seems like they're aiming for a saga from the get-go, and if we're fortunate the sequels will be more than an afterthought.