It's only really been in one of the latest games that a way to move the Lifestream to another planet was part of the plot (Dirge of Cerberus's main plot is preventing exactly that being prematurely set off by a madman), though Spirits Within (the first FF movie) had something like, but the alien Gaia (planet's soul - same thing as the Lifestream) was kind-of a ghost.

But anyway, it's certainly not for every planet - the FF worlds may go about it once every few billion years, but other planets... well they may find other ways to stay around. The sentient stars may look forward to lives as pulsars, neutron stars and black holes!