Isn't the point of insurance to manage the large variation in time between your consecutive covered events?
Suppose your house would cost $400k to rebuild if it got destroyed, and the average interval between things happening at your location that would destroy it is 1000 years.
If those events happened regularly every 1000 years starting from the year you built the house then you could deal with this simply by setting aside $400 every year in a house rebuilding fund.
But if those events occur more randomly, still averaging 1000 years apart but with a large variation, that doesn't work. If you want a 99.9% chance of your fund not going bankrupt and we assume covered events are normally distributed you need a very large fund.
If you have 10000 houses still each being destroyed on average once every 1000 years, and contributing annually for each house the same amount as under the "everyone handles it themselves" scenario, then thanks to the Central Limit Theorem the size of the fund you need is way way way smaller than the combined sizes of all the funds when each house is handled separately.
Note there is nothing in here that requires the same annual contribution for all houses. What is required is that the total annual contribution matches the total average annual loses.
There may be good policy reasons for requiring some kinds of insurance to charge the same amount to everyone, or at least to group people into broad groups where everyone in the group gets charged the same.