Just Attacking Is Boring
You are 100% correct. The key to fixing this is to make the stakes interesting, and to do things besides attack.
Stakes, Stakes, Stakes
No, not the kind you use on vampires. A good Fate conflict should be about something. There should be something you gain if you win, and something you lose if you, well, lose. And the other party should be in the same boat.
Or, to put it another way, why isn't at least one side fleeing?
This article explains it a lot better than I can:
Don't Just Attack
Just attacking is boring. It's also ineffective. Create Advantage is your friend!
Create Advantage has a few, well, advantages to Attack - mathematically, it's got slightly better return on most rolls, and it also lets you choose the skill matchup to a certain extent. Going against the combat beast with +6 Fight? Not a great idea. But if he won't Notice you Sneaking behind him, you can use that to advantage yourself.
Beyond that, the narrative truth of aspects is your best friend! If someone is Trapped In A Web, that's going to make it impossible for them to do lots of things, and will make other things much harder to do as well (modeled as Passive Opposition).
Once you and your players grasp this, Fate combats will switch from a bunch of boring attack rolls (which will tend to have little or no effect between the top combatants, anyway), and become a constantly shifting battlefield of one-upmanship and trying to get the upper hand. And that can be pretty interesting.
Fate is heavily influenced by Amber Diceless. And in Amber, the character with the higher skill wins. Flat out. Which is even more boring than just rolling Attack!
So the game in Amber is to manipulate the situation so that you're either comparing different skills, or so that the situation is so lopsided that the difference in skill is irrelevant... and that's what, in Fate, Create Advantage does.