Cutting away the high risk, low payout parts of the insurance decreases the number of payouts significantly. That does mean variance in payouts goes up.
So, insurers will either need to find lots of new customers to get N up again, or relatively high amounts of capital to survive those high payouts.
If they think they cannot find those customers, they need more capital. To finance that, they need more income, which means charging you more, which means fewer customers, which means charging you even more, etc.
I'm sure you get that insurance through Lloyd's, but it wouldn't be cheap.
I'm fairly certain there are policies designed for high net worth individuals who can cover the first million in losses themselves but don't want to be exposed to long tail risk. I've definitely heard people talking about it, particularly for real estate.
If reinsurance is available to insurance companies there is nothing in theory stopping it being available to individuals. This sounds like a market that is ripe for disintermediation.
Thing is, insurers live by the law of large numbers (https://en.wikipedia.org/wiki/Law_of_large_numbers).
Cutting away the high risk, low payout parts of the insurance decreases the number of payouts significantly. That does mean variance in payouts goes up.
So, insurers will either need to find lots of new customers to get N up again, or relatively high amounts of capital to survive those high payouts.
If they think they cannot find those customers, they need more capital. To finance that, they need more income, which means charging you more, which means fewer customers, which means charging you even more, etc.
I'm sure you get that insurance through Lloyd's, but it wouldn't be cheap.