I guess my next question would be, is it possible to make combat exciting through narrative while still just using the same attack and roll for damage sequence?
That depends what you mean by "through narrative".
It might help to look at other games for this.
Take one of the simplest games out there - Fate Accelerated Edition. In FAE, there's to basic actions in combat, that are most relevant to this discussion - you can Attack, or you can Create An Advantage.
(folks who know FATE know where I am going with this, and can skip it)
If you Attack, there's an opposed roll. Typically your attacking trait plus 4dF (a dF produces a -1, 0, or +1). Whoever scores higher wins, and does Stress (the game's form of damage) to the other. You can just attack each other back and forth, and eventually someone will win - typically whoever has the higher attacking trait, but it can swing a little with luck.
But like in D&D, this isn't terribly interesting.
Thus, you can Create an Advantage. The Advantage can be pretty much anything you can think of. Say, you want to toss sand in your opponent's eyes. You roll to Create the Advantage "Sand in their eyes". If you succeed, you can get a +2 on another die roll for which that makes narrative sense that it would help. YOu could, say, throw Sand in their eyes, then get a +2 on your next attack. Or some other party member can get that +2, as they are transferrable advantages.
The typical way to beat a tough foe in FAE is to have the party build a bunch of narratively appropriate Advantages, and then someone who is good at fighting uses several of them at once (they add together) to generate a very high Attack result, and do a load of stress all at once.
So, the way to win is to
build up the action with advantages, and then use them to beat the enemy.
In a sense, this is tactically uninteresting - each thing is really just a +2. Generate enough of them, and you win. But it is tied to narrative in an entertaining way. And the GM almost never has to say "no, you can't create that advantage", because they are all worth the same amount, so no one of them is going to break anything.