TL;DR
"Connect to Address" is quite simple and could remember more than only the lastest address used.What ?
My suggestion comes with two levels of implementation to improve the experience with multiplayer (re-)connecting to a private server:1. Remember the password from the latest address and try it, if the address have not changed.
2. Extend the "Connect to Address" to a collection of private servers the player can manage. (Best: steam sync of this collection)
Why ?
If a player is playing a lot on private servers, he has to remember or keep track of all addressess and passwords.Reducing clicks and keystrokes to (re-)enter a private will bring more joy to those playing a lot on private headless factorio servers.