I tried that a couple of times, but the problem I had is you click to combat the unit and *nothing* visually happens - the game instantly zooms in on the next unit to move. I'm left with no idea what the result of the combat was. (Yeah you get the notification up in the top left of the screen but that area is usually filled with notifications coming in and it's not always that obvious which one relates to that particular combat). I could really do with a 'quick combat' option that doesn't work through the motions of the combat, but does at least pause for a second or so to show you the result.
The other thing I find that slows down my game a lot when I'm warring, and I wish I could figure out a way round it, is Civ's rather unintelligent selection of units to move. I often find I start a battle, but every time I use a unit to attack, instead of then selecting the next unit in the battle, the game zooms in on some other unit at the other end of my empire, so half my battle-time is spent re-focusing the map on where the battle is. That's often quite a drain on time. I often find myself wishing that the game would intelligently order the unit cycling so it prioritizes units nearest to the one you just moved. Lately I've found I can partially solve that by using shift+click repeatedly to select all the units on a tile that I want to move then, having selected them all, click to separate them, but that only works for units that are on the same tile at the start of the turn. And the fact that if you have a lot of units on a tile, the game uses scroll bars to show them all doesn't help as you have to keep scrolling to see what's there.
All in all, I do tend to feel my game often gets slowed by the rather poor user interface for selecting and moving units.
(I also tend to wish there was an option to do all the workers first, for those times when you're building a road for your units as they travel).
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