I have to agree with those saying combined arms is possible and more devastating.
I have some all cav games. And yes, they do rock. But are expensive as hell and take casualties. (Annoyingly, it seems like my top tier stuff like Hero adventurers and other maxed out types die more often than they're saved by wounds, yet low tier ones rarely die and always get wounded. This holds true in my infantry games too).
But my combined arms game? Running a roughly 1-1-1 split on Inf, Cav, and Archers? There's many battles I can win with less than 10 casualties. The archers (A mix of Pendor sorts, Barclay Sappers, Merc crossbowmen and armored crossbowmen, and Ravenstern Rangers currently) - (They also tend to get some more haphazard, depending there they're deployed, support from my Jatu, Singalian, and Adventurer cavalry troops, but I never count on this, though probably should be more creative with it)... but anyways, the archers can many times do the job on their own depending on the map, though when the enemy gets too close I'll order a charge of my Infantry and Cavalry to finish things. Only armies with strong heavy cavalry with shields ever does a lot of damage (Jatu, mainly). Can't wait to get some Noldor Warriors added to the mix, 30 of those and... yikes. Yeah, I doubt much will matter. And I'm definitely saving three Qualis Gems for as soon as the Noldor City is open to me and getting 45 of them right then and there to mix with some Barclay Sappers (If I can find anymore of them. My glorious original 37 I found early on has slowly wittled down to only 9.

) and watch my enemies fall before me!
My other main game currently has me running about 2/3rds cav, the remaining third archers, mostly Noldor. Order the archers to hold their ground near the deployment zone (Preferably on a hill) and have my cavalry follow me for sweeping charges. This is nearly as devastating most of the time. But my cav tends to take a lot more damage.
And I've seriously destroyed Jatu armies by kiting a Noldor PATROL into them (That was hard) and joining the battle with the Noldor and watching them mow down the Jatu charge like they were the Light Brigade charging into the Russian's cannons. It was sick.
As for the uniques. In general I've found the Adventurer stacks and Jatu to be the worst (Well, and Noldor as well. I just try to drag Jatu armies towards them until they're manageable :p ) - though Heretics can be ROUGH when the freaking Demonic Magnuses are spawning in droves.
And Snake Armies are wimps.
EDIT: and I completely disagree about larger battlesizes being a 'cheat' - if anything I'd say smaller ones are cheating. As others mentioned, much less player contribution the larger they are. Leading to more of a necessity of using tactics to make up for things needed.