I use vim to be prepared for a new server, but do not stay with screen to be prepared.
I only once had a need (easy copy paste in terminal) to get tmux running on a server with no SSH, so I installed it.
For all other machines, which do not have tmux installed I use my local machine and SSH/MOSH with my local tmux. If there is a need to have a long running command on a server, I use tmux to detach the session, fallback to screen for detaching, fallback to SSH nohub