You don't seem to realize several things. First that XIV's story has put great emphasis on the player character being an exceptional adventurer and being the beacon of hope to saving the world. When you put that next to a character like Lightning/Cloud/Zidane/Ramza, the chances of them stealing the show and making you look like a chump are ridiculously high.
Second, it's no secret that SE is in love with Lightning and has been shoving her down people's throats. Sure, FFXIII was liked the home market (AKA Japan), but there are also people who see Lightning as the closest SE has ever gotten to the quintesential "strong female character that's not strong on her own merits and concept, but because the author/characters tell you how strong she is and is given constant pushes in an attempt to convince you how strong she is". With that in mind, I highly doubt SE would do the right thing and have her placed in a support role (similar to Thancred/Yda&Papalymo/Y'shtola) during this proposed story arc.
Thirdly, the reason crossovers like this are so risky is because they do threaten whatever you attempted to establish prior. This is why Cloud (and later, Balthier) entirely faded into the background when they crossed into FF Tactics; they became minor players in the larger campaign led by Ramza. Cloud was also nowhere near the most powerful character in Tactics (Orlandu, Beowulf and Agrias could easily wipe the floor with him). Again, I don't see the writers putting Lightning in a minor role when this is obviously an attempt to use FFXIV to advertise the third FFXIII game. Their main goal is to make Lightning look good, and it may come at our (characters') expense.
That's where the hesitance comes from. And I would react no different if it were Locke or Faris or Luneth instead of Lightning.