Hmmm..Years and years down the road, when we're non exsistent..possibly, but I doubt the government would cut AM/FM transmissions altogether here. Especially when it's often used as a platform to boost one's political agenda or political party for that matter in this country. Also independent artist, record labels, and major radio ad spenders (ie: McDonalds) would raise more hell than radio corporations if the idea even arose. Can't speak for UK, but I think it has more history, tradition, and value in the US. No it's not the same "must have/ can't live without" medium as it was even as little as 10 years ago, but it's a option.
I do foresee the day years from now when AM/FM won't be an option in cars anymore, but we all know that change is constant. It's how you adapt, innovate, and overcome the situation - that really matters. Prime example of that formula recently local tv channels have been scrambling their brains and pouring millions into upgrading to new in house HD technologies, becuase their signal would be useless whenever the gov't plans to switch over to a require HD transmission.