*Edit: Oops I guess you meant primary series but I can't understand the logic behind that if they're willing to do ports and remakes of games on just about every platform and also have a multi-platform game in development for the PS3 and 360 and have mentioned that the Unreal 3 engine keeps down costs, that it would be so impossible to believe that they'd make other multi-platform titles. I mean if Capcom is now doing it with their Resident Evil franchise and many many other developers are making multi-platform titles with their major series for the PS3 and 360 why not Square? As for them not breaking traditions, I remember people saying they'd never leave Nintendo's platform (that was right up until the big FF7 shocker was dropped on the public).
Well their remakes are usually to build interest in new systems that they intend to focus development on. For example they remade a lot of their SNES games into PSone collections when they switched focus to the PSone. They remade a ton of games for the DS when they shifted primary focus to it as well. But notice, even their remakes of these games are exclusive for their generation. The PSP remakes and the DS remakes do not overlap. You have a point though that at the moment they could be shifting to a time when they are willing to make their primary franchises multi-platform, which would be HORRIBLE news for Sony as I can guaruntee if they do it with Kingdom Hearts, they will do it with FFXIII as well. Which will literally mean the end of the Playstation 3. They don't have a tradition of single platform loyalty, but they do have a tradition of single platform exclusivity for their primary game series. Obviously they aren't single platform loyal. Anybody can go to wikipedia and search the game release lists and see there are a lot more DS games than PSP games, including major games.