There would really be no point in this. As it stands, no team should have to lose a franchise player or two. It's the supporting cast that takes the hit. In fact, many teams already do the 'franchise' player thing, whether its a young guy like Bergeron or Nash, or more experienced vets like Richards/Lecavailer, Elias, Luongo, etc. Once you make that initial big $$$ investment on a player, even if they hit the UFA market, if they're happy with you it's not going to be hard to retain them.
Like say Rick Nash, making $5.4 mill for the next 4 years. I don't know if he'll be a UFA at the end of that, but it should be close, even if he was though, it's only going to cost them another million or two to keep him, if they're close to the cap then it just means they'd have to lose a Carter or Berard, not Nash. And having been treated well by the organization there should be no reason why he'd want to leave.
Only thing the cap does is prevent teams getting too many 'franchise' players.