Well evidently it's a condition of renting the theater. Boo hiss.
The Met Opera is not renting the opera house. It is their home base. Ditto with the organizations at Avery Fisher. The facility fee is just another way of squeezing additional income out of the customer, but hiding the additional charge until the end of the purchase transaction.
Interestingly, a glance at the Annual Report for the Metropolitan Opera 2009 (available on line) lists "Opera House" as an operating expense. The number given is 18,509. Million?