"When in doubt, have a man come through the door with a gun in his hand."
That's something out of Raymond Chandler, one of the early pulp writers, but it might as well be Fate GMing advice. (I think it is, somewhere, but I went looking for it in Spirit of the Century and found only ninjas.)
Putting aside any issues of what happens when you use magic to murder someone (which as I understand in the Dresden Files universe is a Very Bad Thing) the deal is that your previous GM played an investigation where you tracked down a supervillain without starting any fights.
What a convenient universe that must be, where fights only start because the PCs decide to start them.
On Combat and Character Development
Combat is not a mysterious place, not of this world, that you access through a screen transition. It's happening in the same place everything else is happening, and people there are the same people they are outside it. All your Aspects are still present, all actions still exist (though you don't have time and care to, like, do research or painstakingly craft something).
So if you want to use Empathy to deliver a heartfelt friendship speech that stacks a couple invokes on somebody else's Aspect, knock yourself out. If the bad guys have some horrendous secrets they want to lever to deliver a psychological blow, they can hurl them in lieu of bullets.
It is true that combat doesn't really lean into character expression the way more free-action events do. If you're in combat you don't really need to talk about how you learned to punch someone or where you learned to aim, Fight and Shoot will work at their listed numbers without, in most cases, any justification. And it's really easy to just get drawn into smacking numbers against other numbers and forget that there are actually people doing the shooting and getting shot.
So... don't forget that? You're still narrating the results after all, every punch, every shot. It doesn't hurt to ask people for a little more description than "I use Shoot on the army of vine-men" so you have something to bounce off of.
On Player Desires
Not getting in fights isn't the same as not starting fights, of course. There are good reasons not to start a fight and leave some other human being who hugged their kids and petted dogs and said "please" and "thank you" to bleed out in some forgotten corner of the world.
Fate pretty explicitly tells you to sit down with your players and talk them through what they expect of the campaign. Places, themes, their own characters. So while you're doing this it's important to talk to people about what kinds of action they expect out of the game.
Does your combat player want to be strong? To like, be the guy who catches a falling rollup door or desperately holds the rope while everybody else is dangling on a helicopter? The guy who cracks his knuckles in a hidden corner and drops the guy who was waving a gun at everybody else with one punch? Or do they want you to tell them what happens when they murder other human beings?
It's probably a little more of the former than the latter. But at the same time, it's important to listen to what everybody else expects from the campaign. And to raise your own ideas, about how this time around, every now and again, a man's going to come through the door with a gun in his hand.