Right, but countries that are in lockdown or semi-lockdown are haemorrhaging cash because loads of businesses are closed or only open at greatly reduced capacity, loads of workers are on furlough or simply unemployed, plus it's hugely expensive to treat all the sick people. I can't see any real reason why governments wouldn't want get everyone vaccinated ASAP so they can get back to earning and spending money.
I don't know about America or Israel, but I've seen even people who are strongly anti-Brexit saying that being outside the EU's medicine procurement scheme may actually have helped us to roll it out much sooner.