There already have been story updates, and will be more in the future, but we have to unlock the map to GET to them. Right now we need to liberate the areas that used to be our old stomping grounds so that we can do things there again. Can't have heartfelt reunions and wholesome dates with the girls when they are under siege by enemy forces and our date spots are smoldering ruins overrun by hostile broccoli.
It has been mentioned in the past that Chapter 3 is going to be the final installment of Corrupted Kingdoms. This will eventually end the game (though a Corrupted Kingdoms 2 has been promised in the distant future), so yes there will be much more here than just combat. But right now, week to week, combat is what we're getting because that's the part of the story we're in. That's what he needs to develop to get the game world back to a state where we can have other things.
The best method for you may just be to step back for six months, go play other things, and then return here at the end of the year or next year. At that point there will be much, much more unlocked for you to do; both combat and non-combat. It'll definitely feel like a lot more significant and varied progress has been made.
Or you can just keep being impatient, like me, and still check the weekly updates waiting for the chance to reconnect with your favorite girls (and punch Morgana in the tit).