This is what insurers already do. Using whatever information they can get on all their anticipated customers, they make it so the expected value of your costs is less than the expected value of all your payments. Going purely by expected value, insurance is a losing game for the customer.

The reasons it's a great idea are (1) you don't get to borrow from your future savings account's balance, and (2) insurers often encourage not-totally-rational customers to practice better habits to reduce costs. The first point is what customers want: avoidance of bankruptcy.