Why would we need a president? I'm not even convinced that we need a second chamber in Parliament. The elected Parliament is sovereign and that's the way it should be. I don't like what the current government do/have done, but I am glad they get to enact their programme, as they were elected to do. Biden, on the other hand is hamstrung by the separation of powers, just as Obama was.
Plus, the idea of a president is intrinsically a nod to the idea of a ruler. a leviathan, a superior being. That's what we want to get away from! We need to have confidence that we are grown up enough to rule ourselves without elevating or genuflecting to anyone.