I did some thinking about a potential replay function. Here is a very primitive mockup of a button that toggles open a menu.

The lower controls could let you do stuff like replay, choose the speed of combat, or even pause and move forward or back a step? The controls could be more or less granular.
I didnt put a pause button in this mockup, but in order to read what is happening in the top part, a pause button may be required.
The top section tells you what is going on in greater depth, and if any keywords show up there, you could click on those to get further information as well.
I guess after the 100th combat you would probably toggle the information and controls off, but it would be very informative in the meantime)
The main thing, besides the toggle button, controls and description area, would be the fact that you would have to click a button to confirm when a combat is done. This would be required, because when I am playing and a combat goes by that I was like "what the heck jus happened?!" I would want the option to hit replay at the end of combat to get a closer look.
Would that button be so bad after every combat? Probably not, but it would slow down things a bit. Maybe thats a good thing.
Another way to get more information of what is happening during combat may be to announce the damage done by an attack or ability.
The information goes by very quickly on Super Auto Pets, but they do announce the damage in big red numbers. If 3 Mages cast a fireball in KH, it would maybe be nice to see that damage number.
... and, I never noticed it before, but SAPs has a few replay control at the top of their combat screen. I might prefer the buttons under the combat tho, closer to where the mouse or hand is usually resting.