Of course something like "exec /usr/bin/screen -xRR" in your .bash_profile or whatever does roughly the opposite, which is also cool, because you can attach multiple devices to the same open screen session simultaneously.
I believe if its in .bash_profile you want it in a "if [ -n "$SSH_TTY"]; then stanza, it was something about scp or running commands in a ssh commandline would misbehave. One of those things you set up in you dotfiles in the 90s or whatever and forget why you did it.
check the manpage search for options xRR it'll show up.
-x attaches to a non-detached session aka multi-display mode, stereotypical pair programming / tutorial / support use.
-RR reattach and if necessary detach (overridden by -x above) or create it (as happens on first login after a reboot) and use youngest session if multiple sessions somehow accidentally get opened.