Did I say you can't pvp on Lordaeron? Sure, you can, but you can't get relentless weapons for free.
What can you do on Lordaeron that Blackrock players can't do? You can get the BIS pve weapons, off sets and trinkets in the game by doing pve, without the need to climb the arena ladders or reaching a certain arena rating.
Trust me, you don't want to use relentless weapons to top the battlegrounds charts or to win them. Do you want the relentless weapons for free? Play on Blackrock. It's not rocket science.
Besides, I am wondering why someone, being aware of the cross-realm system, would play pvp on a realm which has been created with the precise intent to give the players an harder pve content (which is definetly not "blizz-like", according to the 3.3.5 patch), thus becoming the very cause of his own demise.