Pretty much EVERY mountain in the US requires a restraining device on your equipment (brakes, leashes, something like that). Most just won't let you up the lift, some will actually call the police and charge you with reckless endangerment (this is EXTREMELY rare, and is usually because the customer is being a dick when asked to leave because they don't have brakes...but it can be done).
Not to mention, for most bindings, the heel of your boot rests on the brake of the binding, without the brake you'll find yourself pre-releasing much more and you'll experience heel wiggle with the platform the brakes give you.