Well, the first thing you have to understand is that the insurance company doesn't have to pay you anything or explain anything at all to you nor do you have any standing to appeal anything.
You are not the policyholder.
Many insurance adjusters (including me) will discuss estimates with contractors as a courtesy to their policyholders but that is not an entitlement.
It's ultimately up to the policyholder to deal with his or her own insurance company when there is a dispute about payment for repairs.
If it costs X dollars to fix the damage and the insurance company doesn't want to pay X dollars, the policyholder has several areas of recourse against the insurance company.
But to answer your question, yes, there are plenty of laws and regulations that address overhead and profit. Contractors charge it and insurance companies pay it. That's the nature of the beast.
The insurance company that doesn't pay it is not only an exception to the rule but runs the risk of breach of contract and bad faith lawsuits as well as sanctions by insurance departments.
There has been much litigation against insurance companies that mess around with overhead and profit, including several class action lawsuits against major insurance companies.
Here's what the Texas Dept of Ins has to say about it:
And here's an article on some of the lawsuits already in progress: