tmux solves the session resumption at a lower level. You can have a connection from home, jump on a train, open your laptop and keep typing and do the same when you get into the office. You don't need to re-auth each time (or deal with delayed disconnects).

It works well WITH tmux, not instead of tmux.

Which means your solution would be something like:

  while true; do
    ssh -t ${HOST} tmux a
  done

But that lacks the other benefits, especially having to wait for the session to timeout.. Take a look at: https://en.wikipedia.org/wiki/Mosh_(software)#Performance