I play both kinds of strategy and I'm the same way with RTS. I don't know why, but I just prefer to do whatever I feel like doing over winning. I'm however, not a competitive gamer in any sense besides messing around with friends.
One of my favorite RTS games, Age of Empires 2, tries to create an environment where players have to think, but it really only boils down to catapults kill guys with swords, guys on horse kill catapults, so you send in some guys with spears to kill the guys on horse, so your catapults can kill the guys with swords who kill the guys with spears. Basically the strategy is the same, a cluster of guys of slight diversity.
Actually, it all comes down to typing Ctrl+C and entering "How do you turn this on?"
If you have never done it, do it now! Ages of Empires is awesome!
OT: I never really thought about it, but you have a point.
Company of Heroes!!!!! :D
Men of War, good luck rushing a MG or mass tanks and try to rush well placed AT.
This is why I favor the total war games. Positioning, type of units, experience of units along with the skill of the general all factor in how a battle goes. Only a few units are capable of holding out for an extended period when outflanked and even less will fight to the death if they have an avenue of escape(this is why completely surrounding the enemy is a bad idea).
In more recent games, it's less about unique unit compositions than it is about using them correctly. Shogun 2, for instance, has a counter mechanic where sword beats spear, spear beats cav, and cav beats sword. Naginata is kind of an all-rounder and missile units are useless in melee but effective against lightly armored infantry and fairly effective against cavalry provided they don't have the skill to dodge volleys.
I do disagree with some of the OP though. High level play in Starcraft 2 that I've seen requires great skill in micromanagment of units in a battle. Good micro tends to get you the most out of your units, though the right death ball usually does the trick in all but the highest level of play.
I can also recommend Men of War, based on what I've heard and Company of Heroes on personal experience. Ruse was interesting based on the demo I played, but it never seemed to get much beyond research better infantry and ambush any armor you find... till your enemy made artillery and beat the hell out of your position.
Most RTSes seem to amount to, build up as many units as you can, zerg zerg zerg. I don't know, I don't really play multiplayer so maybe it's different...?
Uhhh, I have nothing good to add to this thread, but I suppose Valkyria Chronicles has SOME tactical elements in it. I mean, the A.I. is generally a crapshoot (I've won purely based on enemy incompetence), and the most tactical element is perhaps planning for inevitable surprises in later scenarios, which is really only effective on your first time playing a mission and if you aren't a reload whore. Beyond that it's more just identifying the most efficient way to kill your enemies/capturing their base, while deploying your troops in a way that minimizes risk and utilizing orders when it's appropriate. At "higher levels of play" this often comes down to one or two units nimbly infiltrating the enemy base and capturing it without much fuss (which is where the "tactical" elements really break down). Though I'd say that's fun in its own right. Given that you're never dealing with very many units on limited maps, variables the game throws in are more like obvious gimmicks that involve (yes/no) choices or clearly preferable courses of action than actual strategic factors, and much of one's success can come down to accuracy/evasion. Overall, a fun game, with light tactical elements. Of course, refusing to allow any of my units to die probably amplifies that just a bit (they all have individual personalities and such). I'd say it requires at least some forethought, so it's not an utterly mindless experiences. Probably no better, if not worse, than the games you were complaining about in your OP. It definitely employs those rock/paper/scissors style unit types. I'd call it breezy, but battles can go on for a little while, so it involves a degree of time dedication.
Oh yeah, don't play it if you hate the mawkish sentimentality displayed in a lot of anime. The story and characters still manage to be saccharine and rudimentary in their execution, despite dealing with some genuinely heavy themes.