You don't do anything else when playing a turn based game like this?
Any game like this you have other stuff to do while you process those long later game turns. Could be a show/movie you're watching, tabbing out to watch YouTube videos, doing chores, etc.
If a game forces me to play another game or do something else entirely while waiting, the game has serious issues.
I want to focus on the game I'm playing - only exception I can think of is multiplayer with other people and you have to wait for them sometimes, which is fine of course.
Either way, that's not the issue here, AI turn times are almost instant for me.
My issue is that actively focusing on doing just a single turn takes forever (once a certain size is reached), making the game grind to a near halt.
And for Dominions, that is mostly due to a lack of automation.
Btw, the issue with the mage auto search not working has apparently been fixed, at least it works for me now.
Which is nice. One menial task less to manually fiddle with.
But there are still plenty things left that are no brainers and could/should thus be possible to automate away.