So SC2 starts off with SCV-auto split, no more manual splitting at the start of the game (all players now can play the first 5-seconds of every game like a pro: no practice needed anymore) But then muscle-memory people wanted an edge, so they added MULEs / Spawn Larva / Chronoboost, giving players a muscle-memory / simple timer countdown to play with. Etc. etc.
Just back-and-forth changes like that was the real problem. The general balance patches had no idea for the final metagame they were actually going for. Did Blizzard want a game that rewarded manual effort (Juggle MULEs?)? Or did they want a game where manual-effort was minimized (Auto-Worker Split?)
In the end: Blizzard wanted both, even if the two designs contradicted each other. You really can't please both groups of players, but by switching back and forth between the two designs, they only really pissed off both camps over the long term.
Starcraft 2 added "Archon Mode", where you can 2vs1 (Weak+Weak player vs Strong player), controlling the same team. There were far more opportunities to play teams in Starcraft2 than Brood War.
And the 2v2 was always an option in Starcraft 2 anyway.
While neither game is perfect IMO, letting the game mature without micromanaging it was a very important aspect of SCBW's success. Instead of mucking with units on a monthly basis they let things simmer and ultimately let balance be achieved through proper map design used in the competitive scene.
In my personal opinion one of the biggest faults with SC2 was their unit design philosophy. The idea that every unit was viable or had some special unlock created a balance nightmare. Its been years since I played either game competitively (played iCCup in BW / Collegiate StarLeague for SC2:WoL) but I remember always feeling like the game had too much "gotcha" in it that SCBW never had. Didn't scout proxy reapers? gg. Didn't scout fast void? gg. Didn't scout x? gg. It was too much rock-paper-scissors where missing one piece of intel was death while SCBW wasn't entirely the same. Taking the Terran/Protoss matchup for example you'd typically expect the early game to be vulture+tank vs. zealot+goon where if the terran player just a-moved into the protoss it was guaranteed loss, but microing the vulture and tanks gave you the chance and arguably the upperhand where the skill of the either player determined the outcome. SC2 didn't have that to the same extent.