My headcanon is that if the Enterprise had kept Scotty with them or taken him to a Starbase, he would get bogged down in Starfleet bureaucracy and regulations. He's not going right back to being a working engineer on a starship. They'd probably make him go back to the Academy and requalify, ideally with an eye to just keeping him there in a teaching position.

He's probably be a minor celebrity wherever he goes, if there are plenty of places within shuttle range for him to go then I bet he's happier tooling around in the shuttle. He can come in when he's ready.