My life insurance is through Vitality. They give points for being healthy, doing exercise, not smoking, etc. And what do points mean? Prizes! Well, sort of. If you get points you get rewards - free cinema tickets, coffee, money off stuff. If you get points they give cashback once a year and reduce the monthly cost. They just bought me a Brompton.
They are not doing this altruistically - obviously they have done the sums and the chance of them paying out is vastly reduced if you exercise the regularly. Whenever I tell anyone about it the response is "why don't the NHS do something like this?" Surely it would be far more cost-effective to pay incentivise people to look after themselves and not be an expensive patient draining resources. And that's even before you add in the cost of lost working time, the often hidden cost of carers, and the psychological cost of people not being as active, and so on.
Is it motivational? Absolutely! I'm not a total couch potato, but it's quite easy to not bother going out for a ride, put it off to tomorrow. But there's points - yes go out for 30 minutes, perhaps up it to an hour to hit the maximum. Stairs or lift? Points - I'll take the stairs. Sit at desk for lunch, or go for a walk? Points again. I used to think it didn't matter I was 95 kg (at 172cm tall) because I cycled a lot – I'm fit, right? Oh, and I'm big boned with muscly thighs, BMI is a useless measure. Now I'm 71 kg and feel so much better for it. This is not something I would have done on my own.
tl;dr Absolutely the government should incentivise people to get healthy. As long as they can find a way that works, targets the right people, and is non-patronising. That's a big ask but it would benefit us all.