Here's a proposed solution.

Airlines should have an "express" counter. This express counter should be at no charge to Elite members, people flying first class, and people who are late due to some fault of the airline connection (the latter should get a "pass" letting them into this line).

Anyone else can also use this line, but must pay $50 per passenger to do so. Members of the airline's FF program can get one such free pass credited to their account each year they accumalte flight miles on the airline.

Reactions?