Probably it just would have gone to some other state affair. Governments seem to need, from time to time, to make their existence known. If we didn't have a Queen to spend it on, we'd spend it on the PM.
Also, it's a bit silly to say "it could have gone to hospitals in the same area". The idea that money is something individually trackable like that doesn't make sense. All it would have meant is the government would have had 1 million dollars more to spend out of a budget of -- what, hundreds of billions? This is why it's chump change. It's 0.001% of our annual budget, and that's probably a high estimate. Spread out over the years between an actually *expensive* visit by her, it's considerably less than that.