The perfect insurance would know that I was going to have to pay catastrophically large amount and would therefore charge me a catastrophically large amount.
Being prescient about getting the number 4 when you throw a dice means you can assign probability 1 to getting 4 when you throw that dice.
Having an accurate risk profile means knowing the odds you'll get 4 with that dice might be 1/6.4 because you precisely measured the shape and weight distribution of the dice and you can see how biased it is.
Let's assign a cost X for the unlucky event of rolling a 4. You're expected loss is X∙1/6.4. If the event only happens once, obviously you either pay full cost X or you don't pay anything.
If you pool with a large number (N) of people, each throwing once that same dice, then the expected loss of the pool is N∙X∙1/6.4, that is, if each member of the pool contributes their share, the pool is going to be able to pay off the individual losses. Unlucky people are better off because they saved X∙(1-1/6.4); lucky people are worse off because they had to pay X∙1/6.4. Pool members agree on those rules, because they don't know if they are going to win or lose, and their contribution to the pool is smaller than the worst case scenario.
So far so good. I deliberately used the "custom" probability number 1/6.4 to show how arbitrary that is.
Other people might have other dice, each biased their own way.
The expected loss for the pool would thus be X∙(P₁+P₂+P₃+....Pn).
Each person contributes to the pool backing proportionally to the contribution to the pooled expected loss, thus the system still makes sense even on the case of 1-sized buckets.
(Disclaimer: I have no idea what I'm talking about, this is not my field, just an average person with everyday math skills. Happy to learn why I'm wrong, in case I am)
(EDIT: formatting and typos)
The perfect insurance would know how likely it is that you are going to have to pay a catastrophically large amount, and would charge you amount*probability. If probability=1.0, then sure, they should charge you the whole amount.
As the data gathered increases, the probability eventually reaches 1.0. For instance, if an insurance company could legally gather all telemetry from your car at a high enough frequency and cancel your policy at will, then it could determine that your car was on an unavoidable collision course and eliminate losses.
This may sound like a silly thought experiment, but I think it demonstrates that in principle, there must be some point at which we draw the line on discrimination to have insurance, so if you find yourself defending all discrimination then you've gone wrong somewhere. Either there's a principle that has been missed, or it is valid to just set the rules in society that people are comfortable with.
There are, however, situations where the model is a reasonable fit - notably, some aspects of health care, where the approach to the limit proceeds over multiple billing periods. A society can choose to spread the cost around, but to do this under the guise of insurance leads to the sort of incongruities and inefficiencies that are seen in the US system.