Some compilers aren't generally available. Hypothetically, what if ICC wasn't available freely to educational users, but some of the students had side-jobs where they used it?
You can always mandate a large set of compilers, make them all available, and leave it up to the students to determine which is fastest. I think that acheives both the competitive/educational goal and the level playing field goal.
I would definitely ban using any compiler that wasn't generally available to the class, or at least disqualify their output from winning the contest. I'd take a generic approach where it's worded just like that, rather than trying to come up with an official set of acceptable compilers, though.
You can always mandate a large set of compilers, make them all available, and leave it up to the students to determine which is fastest. I think that acheives both the competitive/educational goal and the level playing field goal.