You are mixing things up.

There's insurance which allows you to convert an uncertain danger into a known payment. And then there's welfare and redistribution.

By all means, please run some means testing and give the poor and sick or disabled extra money. Or even just outright pay their insurance premiums.

But please finance that from general taxation, which is already progressive. Instead of effectively slapping an arbitrary tax on healthy people, whether they be rich or poor. And please don't give rich people extra stealth welfare, just because they are in less than ideal health, either.

Just charge people insurance premiums in line with their expected health outcomes, and help poor people with the premiums using funds from general taxation. (Where poor here means: take their income and make an adjustment for disability etc.)

We _want_ the guy who loses 5kg and gives up smoking to get lower insurance premiums. That's how you set incentives right.

> The more diverse the pool, the lower the risk.

No. The diversification comes from the insurance company running lots of uncorrelated contracts at the same time and having a big balance sheets. For that, it doesn't matter whether it's a pool of similar insurance contracts, or whether they have bets on your insurance contract, and on the price of rice in China, and playing the bookie on some sports outcomes etc. In fact, the more diversified they are, the better (in principle).

But that diversification is completely independent of the pricing of your individual insurance contract.

Have a look at Warren Buffett's 'March Madness' challenge, where he famously challenges people to predict all 67 outcomes of some basketball games to win a billion dollar. Warren Buffet ain't no fool: he doesn't need a pool, he can price the risk of someone winning this one off challenge.

More generally, have a look at Prize indemnity insurance https://en.wikipedia.org/wiki/Prize_indemnity_insurance which helps insure many one-off events.