The Brood War Air Inference
"The supporting air units (Corsair, Valkyrie, Devourer) do very well versus the Tactical air units of the other species (Scout, Wraith, Mutalisk). The new units in Brood War are intended to be support units, meaning that you cannot win the game with them. Capital ships (Battlecruiser, Carrier) are equipped to deal with these supporting air units in deadly fashion. The key to retaining air superiority is to be the player with the most balanced air force." - Brood War 'Air Balance Model'
This did not work out exactly as planned. Mutalisks are the only "tactical" air unit which see widespread use in all matchups. Wraiths come second due to their utter uselessness against Protoss (HiyA notwithstanding); Scouts are almost never seen (the most famous use here). But the units are used - when used - as designed. Similarly, the corsair is common, the valkyrie less so, and the devourer rarely used; but all are used to wreck air-face.
The capital ships are a funky bunch; the carrier shows up in 2-base PvT, late-game PvT, and late-game PvZ. The battlecruiser is used in late-game TvT and TvZ. (You will be noticing that Terran air is singularly useless - at best, a weaker and unexplored option - against Protoss.) The Zerg does not have a capital ship - but does have a "capital unit" in the ultralisk. All three units, however rarely used, fit into their assigned roles - Massive Damage - when used.
Ignore the scourge for the moment, sit back, and consider this. My hypothesis is two-fold: A) the races are fairly similar, and B) each race's units are designed to work together.
Racial Similarities
We are misled fairly easy by the race's obvious differences. If nothing else, contrast makes for better theater. But step back for a minute and consider.
Each race has a melee and a ranged Tier 1 unit (marine & firebat, zealot & dragoon, zergling & hydralisk).
Each race has a siege unit (tank, reaver, guardian) to outrange towers, at Tier 2+
Each race got a pair of casters (ghost & vessel, high templar & arbiter, queen & defiler). In each case one is Tier 2-ish and one is Tier 3-ish
Each race has a transport (dropship, shuttle, overlord).
There are of course unique units, playing in each case to the race's "profile". The Terrans have the goliath, a versatile unit (in theory, and in modern mech TvZ); the Protoss have the archon, a beefy unit; Zerg have scourge, a suicide, mass-produceable unit. Terran, weak on speed overall, also has the vulture; Protoss, with no detection besides, adds the observer; Zerg adds another blowy-up unit, the infested Terran.
Brood War, in addition to the new air units and various upgrades, added in a new ground unit (Protoss got a bonus unit) for each race. The Terran medic allows Terran infantry to not totally suck against everything. The Protoss dark templar gives them a pure harass/control unit, approximating some of the vulture's roles. The Zerg lurker - combined with dark swarm, especially - opens up terrain control options previously unavailable.
Each races, despite differences in statistics on the units, all have approximately the same range of options open to them. Each race has harassment strategies - Protoss is drop-reliant, for the most part, Terran has speed-vultures, Zerg zerglings or lurkers, but both can also drop. Each race can control ground: a Terran siege line, a Zerg lurker-swarm attack; Protoss control is mostly negative, removing units either temporarily (stasis, maelstrom) or permanently (storm, which also serves as a space-eater), or circumventing lines (recall, hallucinate), but still there. Carriers, while not universally useful, also control area.
Combined Arms
Each race's unit abilities are not only paralleled in some way by other races, they are designed to work together in an obvious way. I will look at Terran in detail; the racial similarity I mentioned above, plus familiarity with the game, enables extrapolation to other races.
Terran is essentially based on the classic combined arms force brought to us by WWII and the ensuing popular sci-fi (even if it only worked out "properly" in TvZ!). The marines provide the core of "grunts". (Firebats are a concession to SF tendencies to include badass melee units... and because flamethrowers are actual and cool.) Vultures are a clear corollary to modern half-tracks, armored cars - scouting vehicles. Tanks are tanks; wraiths fill the "fighter-bomber" or "air support" role (mainly in theory, unless you're Leta or Lomo, or playing TvT) while carrying the cool factor of the fighter. Goliaths don't quite fit in (although in the expansion they fit the modern SAM-battery role) but what's a futuristic game without mechs? Science vessels fill a need for a caster while providing some echo of modern aerial scouting. And ghosts - well, "covert ops" says it all.
Obviously the parallels in other races aren't exact; carrying these ideas over to the other races resulted in some oddities. For instance: it's clear now that nobody thought out the intricacies of, "Huh, Protoss's siege unit is badly outranged by the sieged tank" - though I doubt anybody anticipated the battle-shuttle micro of Zileas (to say nothing of Stork) either, so these things balance out.
The "Accident" Theory of Game Design?
In contrast to some other games, though, the thought put into the layout of each army, and its contrasts, clearly doesn't match up. Age of Empires - Brood War's main contemporary rival, if only at WCG - has even more detailed tech trees, more exactingly calculated differences, and more basic similarities between the races. Why was it not the same success? Accident? The fact that Korea chose Brood War, for whatever reason? There are subtle things that can be pointed out. AoE graphics are equally good, sometimes better, but lack some clarity (including clumping up of big formations). Each civilization has maybe too much similarity, making the differences that much more influential and actually harder to balance. Homeworld - a game, surprisingly, from the same era - has much better graphics (to say nothing of its sequel, Homeworld 2, which has still better looks), and gameplay which would have been simple enough to balance out if it had ever made it mainstream... maybe the graphics were too much.
So yes, accident played some role: Blizzard happened to design the game that could be played competitively, with enough similarity to maintain a level field, but enough differences to balance - and, in Korea, what turned into a willingness for the designer to mostly leave well enough alone and let the players get on with the game.
But none of that happens if the game isn't carefully designed in the first place. It may be better to be lucky than good, but if you get this lucky, you were probably pretty good to begin with.
Yes, I Guess I Will Talk About Starcraft II
At first I saw signs that SC2's development had followed some of these same ideas. We really saw the Protoss in detail first, and in that first developer's demo, I was led - perhaps misled - into thinking that the guiding principle was something like, "We have these armies that have been fighting, and they are now trying to fill in the holes in their tactical doctrine." We had units like the immortal, clearly designed as a tank-buster. We had the reaper, clearly designed to improve on the vulture's performance as a raider, while taking some of it's ground-control role (D8 charges) without producing quite the static lines. Also to re-emphasize infantry in the Terran arsenal. Other ideas seemed and still seem a little more random, but it still seems safe to say there was some of this element - thought, and combinations of units - happening.
As it turned out, I have another theory that the beta was in fact too public, allowing every idiot like me to say that everything sucked before we got to try it out. If we had discovered the valkyrie was useless after two weeks of play, what would fantasy do now?) What would have happened in SC2 with a little more chilling out about stuff?
Consider reality: the roach-marauder-immortal "heavies" cut into the use of other ranged ground units - one more variable to account for without really fulfilling a new function. A "ground balance model" was clearly intended, "heavy" > siege > light > "heavy", but now it seems the heavies really just kill each other, while the light & "siege" units massacre each other but neither really touches the heavies badly. (And the solution seems obvious to me: make sure the lights are fast enough to kite the heavies, while shortening the heavies' ranges to produce a clear difference in engagement profile and emphasize their "tanking" status.)
In short, I think a lot of the same thoughts went into Starcraft II, but I think there was also too much pressure to "top" Brood War, and the particular design team identified the crucial factor as "cool units", rather than considering gameplay as a whole and strategic interaction.
...Which means, let the two expansions come out, and then its time for leagues to get busy with maps (and given the editor, "patches" of our own if necessary are possible) and fix this game too. After all even Brood War, with Blizzard's patches, only on Blizzard's maps, would still be hilariously bad.