@slag: I'm sure it is, but I think you can make the "3 game investment" pitch without necessarily continuing that series. If they removed the references to the previous game, and tweaked the story a little, they could have easily just made 13-2 part of the main series. It probably would have sold better for it too. It wouldn't have mattered that they played and looked similar either because that's the way Final Fantasy has always been.
Part of the reason XIII-2 was made was as a response to the design criticisms that XIII received, particularly in regards to the linear maps, lack of explorable towns, and the nature of the leveling system, among other aspects. They also tinkered around with other things like the conversation system and such, and in general wanted to make a XIII game that would appeal to parts of the audience turned off by the technical criticisms of the original. Though, they obviously had to have come up with the idea for Lightning Returns in some form early on in development, given that the game ends on a cliffhanger.
And while I'm crazy and totally appreciated 13-2 for it, I think it was a really misguided idea to fix those criticisms in a direct sequel. If people didn't like the first one, why would they play the second? Not only that, but because it's a direct sequel, that puts off newcomers because they'd feel like they have to play the one people complain about to get to the one that's supposed to fix its problems. If this had just been Final Fantasy XIV starring Kerah, it almost certainly would have been more successful. As for when they came up with the idea for Lightning Returns, I can't say, but if they'd pictured the tepid sales reaction to 13-2, I doubt that game would exist.
While Final Fantasy XIII was criticized, it still sold well, to my knowledge. Well enough that a sequel on a lower budget that reused a lot of the assets was probably a risk they were willing to take. If they had made XIII-2 into XIV, I think people wouldn't have been receptive to it, because the franchise has a history of strongly differentiating itself from one primary entry to the next. If people looked at this theoretical XIV and thought, well this plays pretty much like XIII, but with these changes, it doesn't have the same impact as switching from X to XII, or from XII to XIII, or XIII to XV. Not to say that it's not something that the series has never done (the earlier games are much more similar to one another in many of their elements), but their resources at hand lent more to the creation of a sequel to XIII, rather than a full Final Fantasy sequel.
Honestly, the argument could be taken either way, though as a fan of the XIII trilogy, I'm glad they took the path they did.
I was under the impression that while it sold decently, it didn't come close to making back the development costs, which is why they pumped out the sequels as quickly as possible reusing the same assets. Cheap returns for little work.
Frankly, I dislike the direction the series has gone in over the past few years and I haven't been particularly impressed from what we've seen of XV. It seems to be making all the same mistakes, just with a half hearted attempt to return to some of the old mechanics people liked in the past. Although if they've stopped designing their entire games around big and flashy cutscenes, that'd be a start.