If you did that, there would still be very few answers: Juneau, Augusta and Tallahassee. If you exclude Alaska, the answers would become Olympia, Sacramento, Augusta and Tallahassee. Let's face it, the Nearest US State Capitals quiz is the more real brain stretcher!
Having been to both cities, I doubt they'd be in the mood to be excluded :) I met quite a few Alaskans, though, who'd prefer they were a separate country...
unless you really want to push it and create the 'median distance US State Capital' ;)