The point of insurance is to protect against unaffordable losses.
An insurance business only works if the losses are, by and large, randomly distributed and unexpected.
The more predictable the losses, the more an insurance offering resembles a payment plan where you are simply setting aside money with a third party to save for the eventual loss. This is because as losses become more probable, the insurance company has to increase premiums eventually to the point where the sum of the premiums is equal to the losses if the probability of loss is 100%.
This is the current state of health insurance in the US. It is not what would normally be called an insurance product. In fact, quite a few of the stipulations of ACA make health insurance premiums explicitly a tax from the young/healthy to the old/sick. Therefore, the industry term is to refer to health insurance companies as "managed care organizations" (MCOs), some of whom sell health "insurance".
In the US, when you pay health insurance premiums, if you are young/healthy, you are mostly paying for the treatment of the old/sick, and only minority paying to protect against the risk of you breaking your arm.
The profit that MCOs earn is actually more like an administration fee. The US could have implement an NHS style taxpayer funded healthcare system, but the politically viable option in 2010 was to outsource the administration of healthcare (pricing negotiations, healthcare rationing, auditing, etc) duties to MCOs, hence we have a system where the government (or employer) sets the rules, that abide by ACA rules, and then the MCOs execute them.
For example, nearly half of Americans' healthcare is paid by the government, but it is administered by MCOs. The MCOs are not setting the rules, just carrying out the stipulations of their contracts with the government:
https://crsreports.congress.gov/product/pdf/IF/IF10830
Finally, to answer this question:
>What is the point of paying for insurance, then?
If you have future earning potential, or a little bit of wealth saved up, then health insurance in the US is valuable because your out of pocket maximum is capped.
https://www.healthcare.gov/glossary/out-of-pocket-maximum-li...
This is one of the policies that also helps make health insurance premiums more akin to a tax, along with, but not limited to, the following policies:
Age Rating Factors (adds cost to young people's premiums and lowers old people's premiums)
https://www.cms.gov/CCIIO/Programs-and-Initiatives/Health-In...
And insurance cannot be denied to someone for any reason, and has to only be based on age/location/tobacco use:
https://www.healthcare.gov/how-plans-set-your-premiums/