Yes they would be popular, but let me play devil's advocate here.

Ask yourself why haven't they done world pvp servers yet with no battlegrounds or arenas? It's been suggested a thousand times so why are we not seeing that yet? It's because it doesn't make sense to create a pvp server that would have a different set of rules. It wouldn't be the same game. That would be a totally different game wouldn't it? Where would pvp gear come from, instance drops or faction rep?

But wait! What about PVE gear? Wouldn't those be important to? It's hard enough just trying to have a balancing act with this world they've created, and it would be extremely tough to have a different server with a different set of rules. I'm not saying it'll never happen, but this has been suggested many times and there is very little chance of them implementing it in the near future.