I actually don't look at Fabregas as our midfield general at all because he's not that sort of player. He's more of a playmaker than a general. He lacks the physicality for you to call him a lynchpin or general. A midfield general would be someone like Vidal, Ballack, etc. They all have one big thing in common - physicality. You shouldn't expect that from Cesc.
We can't dominate against big teams because we don't set ourselves up to - and because we don't have the right players to. It starts from the back - our centre backs are generally not good at building from the back - the only player that can actually make plays from deep in midfield for us is Cesc too. We have a massive lack of possession-comfortable players for us to go out there and dominate against big teams.