I agree with most of that, we do need a variety and I think we are probably both talking about approaches that would both be successful in certain games.
As for combating Liverpool, I still think having players who are comfortable in possession is the best way to stop them from pressing so hard. I see your logic but I don't think we have anyone really capable of launching cross field diagonals on a regular basis, not do we have the height to actually control anything that lands any higher than the waist up. Of course, if we had technically sounder full backs, those sort of passes would be within our options.
We did 100% need the speed to quickly get the ball into the final third to bypass the press, but we fielded half a team of players who just don't have the technical ability or composure to deal with it. In our current state, I think dropping him to create space for an extra attacker only adds to our problems, purely because I consider only Fernandinho to be good enough to even attempt to control the game from a deeper position, and even that isn't a natural thing for him. Yaya is still our best option in that regard, and while I agree he probably isn't the player he was a couple of years ago, I still haven't seen anything in Sterling that makes me think he's worth being a man light in midfield for. He can probably improve, but until he does, I wouldn't chance it all too often. Not for me anyway.