The "Removing GC Restrictions Will Increase Interest In PvP" Caveat
While I agree removing GC restrictions might help enkindle more interest in PvP, I don't believe it would be the magic fix for one of FFXIV's least popular features. I say that because the Feast did just that, and still only saw a small spike in activity, and even then, much of that was people initially trying to get tomes quickly, without any real interest in actual PvP gameplay. Sure some of us established ourselves and continue to do so as avid PvPers in there, but we were likely the ones doing it even with GC restrictions in place already.
That said, here's a suggestion: As Grand Companies, lore-wise, are comprised of both normal national armies as well as mercenaries/mercenary groups (i.e. FCs), implement a system to allow players to queue in a Mercenary bracket: you will be placed on any of the 3 teams randomly. Allow for light/full party premades, as I'm sure many players have friends they'd want to team with, regardless of what standard they fight under. Now here's the catch: If placed on a GC team that ISN'T yours, you take a slight reduction in Wolf Marks/PvP XP. This is to maintain a balance and not completely kill off queueing for your actual GC. Possibly allow this point reduction to be bypassed if the player queues via a roulette.
Thoughts?