I'd say the perfect RTS have multiple armies with multiple different playstyles each, they might be able to do same things, but they shouldn't be able to do it same way, if they were, why have multiple armies in the first place?
I'm sure it would suit your POV on the matter if, imagine this, soviets had stock infantry like Obers, but would it really be balanced or interesting? I don't think so.
Each army have unique flavor, unique units, unique strengths and weaknesses, unique playstyles and tactics.
Each army suits different players for different, visual and gameplay reasons, each army creates different synergies in team games and so on.
That is a healthy design.
You like something more in another faction that is absent with yours? Play that other army.
No one is pledging a vow of loyalty to death to Hitler, Stalin or Roosevelt, if anyone is locked within single army, its only because their own limited mindset.
@CieZ
Hey! I'm not that bad, at least I can admit defeat when proven wrong, even if my own argument was turned against me!
A very good RTS, no doubt, but I believe there is something better possible.
Planetary Annihilation took the approach of a single army since they couldn't bid the Total Annihilation IP from a studio which still hasn't used it, and hopefully never will given their track record. I love both of those games to death, though.
Now, the balance arguments there were always between unit types, bots vs tanks, because the developers refused to give an overlapping role with the mainline units (dox vs bolo) after they changed the scale up. It was a good thing, though, since they were essentially the same before. However, the other units in their respective trees were hurt because of this lack of a choice. Eventually, they balanced it in a way where Dox was marginally less effective as a front-line unit, but still valuable to mix into the army (mobility and line of sight making it effective raiding and scouting, but worthy enough to DPS the same while bolos take the shots in main army).
We cannot think of factions like this, since we can't control more than one at once.
A better example, then.
In Total Annihilation, the ARM are, arguably, better than the CORE. From the supremacy of the EMG over lasers in the early game, and the FARK over CORE methods of mass producing their respective advanced air fighters. Regardless, a ton of the roles overlapped, and all their units had a parallel in the other faction. They each had their own flavor and marginally different stats, though many were functionally the same. Funnily enough, the Slasher being superior to its ARM counterpart, the Samson, in that it could shoot over wreckages due to its elevated firing port, blunted the otherwise overwhelming Flash attacks. CORE was on the defensive for the early game, but with proper radar support and micro they could beat back the Flash raids and protect their MEXes. Then there was the heavy tanks. Oh boy. The Goliath, the CORE unit, is second to none, having a decent AoE, a super fast build time (though costing a ton of metal), and a boat load of health, it made the ARM tanks pale in comparison. The CORE AK was vastly weaker to its ARM equivalent as a cheap, mainline infantry Kbot, the Peewee, but, the class was still valuable to purchase because of the superiority of the unguided rocket infantry unit, the CORE's Storm over the ARM Rocko. This meant that you'd still see the Rocko for busting up bases (not AK, AK was WAYYYY too bad for even the reduced opportunity cost of going bots for Storms to pay off its dysfunction). The Samson was still widely used and effective despite the superiority of its equivalent. Now, Planetary Annihilation has reached a state on one faction where the classes are more-or-less balanced and maintained on slight overlap, and Total Annihilation reached a state of somewhat overall inter-faction balance with absolute role overlap.
It's not hard to imagine that which combines the best of both of these worlds. Faction equivalents, in essence, don't need to be fully balanced for access and opportunity to give them their niches. Faction equivalents in the core army, additionally, can exist in harmony with maintaining aesthetic flavor, and playstyle flavor. Without intentional role overlap in the core armies, there will be no niche for similar units to fill, as the opportunity cost will not justify the slightly differing functions of the unit behind a commander. Such is the same with buildings--blunt the failure of one units by bundling the cost with another, better unit one is more likely to get, such is like the commanders, yet available to all armies. We just might see an LeHF, since it adds a delicious flavor and performs a slightly, slightly different role than the rocket artillery, IF the opportunity cost for accessing it wasn't so high.
Commanders / doctrines cannot maintain this sort of beautiful possibility, because they are a sort of mutually exclusive balance overlap which must be a bad choice in one circumstance over another.
But all these examples are brushed aside by Starcraft. Brood War did not have equivalents for each faction, it had wildly different flavors and playstyles for them, and it is a monstrously beautiful and balanced game.
The key difference here is that there is no given plausible equivalent for certain units, and, frankly, no desire for them. CoH2 is different in that it's united by real life's plausible equivalents, and more importantly, its commander-only units which, while present in multiplayer, are often times not truly present at all. The possibility of said equivalents is so near, our desire speaks out to them: if only... if only.
That was... too long winded for so simple a response, so, TL;DR:
It is entirely possible to maintain distinct flavor, overall balance, faction strengths and weaknesses, and a myriad of playstyles, with factions that have access to a rough equivalent of all units from other factions, while maintaining intra-faction unit and tier/building balance.