No it isn't. Insurance is about spreading random risk - hedging against unknowns. It is not about redistributing risk from people that are at higher risk to people that are at lower risk.

This statement is objectivity wrong, given that many counterexamples exist, such as purely income-based health insurance premiums in many countries.

That is not insurance. It is a tax.

You're trying really hard to redefine a bunch of words, yet the set of people you can meaningfully communicate with using your alternative language is small, so what is the point?

What drugs are you on? If you pay a percentage of your income mandated by the government for some service then that is income tax. Insurance is a private contract with premiums based on actuarial assessment of risk. This is not some distinction I have come up with. It is what the words have always meant.

I am sorry that you have been misled to think insurance is some sort of government wealth redistribution program but that just isn't so.

They are probably mixing up the different kinds of state-organized social support (one being the unemployment insurance) with "real" insurance business like car accidents or legal responsibility or yeah also health.