The reason for the lack of strategy in most Starcraft games is twofold: rushing and "Big Game Hunters".
A rush attack, meaning a quick attack before the enemy can build his defenses, can end SC games within 5 minutes. This means that the majority of units never come into play because it takes more than five minutes to get to them on the tech tree. The more advanced units would offer "magic" abilities and more tactics, which would immensely contribute to the complexity of the strategies needed to play. Look at xmatts writeup above for a closer description of rushes.
The other reason is that something like 80% of Starcraft games are played on a variant of the "Big Game Hunters" map. These maps usually feature absurd amounts of resources right next to the starting point of every player. This eliminates the need for expansion bases. Also, there usually is a straight land route to the enemy base(s). This eliminates the need for scouting, since everybody knows how these maps look like. It also eliminates the need for air transports.
Because of these two reasons, most Starcraft games are usually short and bloody affairs with everybody pumping out lots of basic units and attacking en masse. You hardly ever see an island map (where the starting bases are separated by water) on Battle.net. Such a map makes rushing impossible, and is played with more complex strategies. The words "no rushing" (or similar) are also scarce.
As an aside: I know people who don't play Brood War because they say it's too complex for them!
If anybody is interested in a long, drawn-out affair on an island map, contact me. Theoretically, I really like playing Starcraft (not that I am any good at it anymore), but I hardly do, because rushes are boring.