Connection sharing and terminal multiplexers aren't mutually exclusive. Let's say that in order to get to 4-5 hosts (which you run screen on) you have to jump through a certain SSH bastion host which you specify using the ProxyCommand directive. You're going to want connection sharing on that bastion host, to make subsequent connections to hosts beyond much faster. If you have to jump through two bastion hosts to get where you have to go (yes I actually have to do this) connection sharing is a must.

Even without a bastion host, connection sharing allows for faster scp from your home box to the target host you're running screen on.