their profit comes solely from them denying claims. if they paid all claims they would have no profit.

Well, yeah. If someone claimed I owed them $20m because their dog died, I'd deny that too (unless it was life insurance for a show dog or something).

Insurance was originally profitable because the idea was to bring in more money than you pay out, but set the margins so it's worth paying for as a service (covering things so the cost of a payout is high to make the service worthwhile, but the chances of actually paying out are low, to make the service profitable).

However, over time you are correct that it shifted to focusing on finding ways of putting profits over quality; which came with all kinds of legalese to avoid payouts, among other things (like rigging the healthcare system so the cost is always high, so their costs appear low in comparison).

So you're kinda right, but you seem to be conflating the American insurance market with insurance as a concept.