Pay for it. Broadcasting the Olympics costs NBC lots of money. These deals are how they pay those costs. (And if it wasn't NBC, it would be CBS, ABC, or Fox.)
One of the hazards of giving up living television is that...you give up live television. NBC is not obligated to do squat for you if it can't make money from you. It's a business, not a charity.
And stop praising the BBC. It's not free. Brits pay a mandatory tax to support the BBC, so it is no different from cable/satellite TV in the U.S.