Crossfit total is basically raw powerlifting. Press instead of bench. Incidentally, the good Olympic pressers pressed 3-4x weekly, and had to clean their presses.
The Crossfit total is the brainchild of Mark Rippetoe, and he's had at least one XFT meet at his place. So, it's a competitive thing. It's not just something that gets tossed out there as a WOD every now and then.
One thing that is absolutely not built by accident is maximal strength. You can get by up to a certain point with random stuff, but that certain point is not going to be very high, especially if you are coming from an endurance background into Crossfit.
Getting and maintaining a high strength base is more difficult than maintaining a high level of conditioning. Arguably.