Does health insurance in the US do something besides risk pooling?

Health insurance plans play a role in paying for large unpredictable healthcare procedures, but also for smaller, more regular ones. For example, the plans I have had have always covered my annual physical. I thought the role of insurance generally was to pool risk, but that doesn't seem to be what's happening here. What other function is my health insurance plan fulfilling that it makes sense for it to cover these sorts of expenses?

I imagine this is the case other places, I have only scoped the question to the US because that's what I'm familiar with.