Well actually I believe there is already a "casual PvP" event that a radio station puts on... I think Inquitar organizes them in a chat channel for his radio show. Also why don't these casual PvP'ers make use of the private challenge system and PvP against people in their own fleet or better yet, in zone on Earth Space Dock. I have had PvP dates over zone chat. I find that role players love to leave ESD for some private challenges on ghost ship (although they probably thought something else would happen in a private map). It's the makings of a bloody romantic comedy.
See, I don't listen to radio shows or whatever. And even though I'm a member of a pretty large fleet, there may be times when not that many people are interested in private matches. I prefer to use the immediately available, easy to go to places to get PvP - the queues and war zones.
I think Mustrum had a point about the population - it's way too small in GPvP. The way it will grow is not by having all the people trying ground out get utterly crushed, destroying their spirit so they leave shortly after trying it, but by making sure they have fun.
Given the fact that last night, there was 15-25 people fighting an impromptu battle in Otha, and one queue popped in the hour or so I was there, I'm betting finding a way for a larger population to not face the same soul-crushing* team again and again is the way to help people have fun.
*I use soul-crushing a bit tongue in cheek there, but let's be honest - it gets brutal sometimes. GPvP has long been the only truly enjoyable thing about STO for me, so I try to be patient and learn, but it gets old sometimes. And even though I could possibly make a difference by taking charge of a PUG against the elites, I usually don't bother, since it probably won't make a difference anyways.