"Insurance is ALL about spreading the risk. Over the population and over time."
You're forgetting the all-important homogeneity of the risk pool (over the life of a contract, usually a year or few -- not a lifetime!). Different risk pools naturally get different premiums/benefits, at whatever level of granularity the marketplace can offer. Guess what industry was just stopped from being such a marketplace (web site nicknames notwithstanding).
"An Insurance plan is intended to insure that you have an organized way of putting aside money, that it will be invested by the insurer to permit the insurer to be able to make a profit on that money (and maybe even return some of it), and finally, to deliver if and when you need the money."
No, an insurance policy is not a savings vehicle. Even life insurance isn't, since the actuarial premiums on average are in excess of the expected payments + investment returns (all numbers suitably discounted), or else an insurance company couldn't exist as a going concern.
You might like reading Warren Buffet's annual note to his BRK investors. He gives a basic introduction to the concept of insurance, which you appear to sorely need.