Insurance companies use "float" money taken in from premiums. Even though it is not their cash they invest it as long as when needed they can pay a customer claim. Could a non-insurance company that gets funds from customers for holding then create a similar scheme to use these funds for investment as long as they have the funds available when the customer needs them. I would believe the company would have to have full disclosure but if they do, is that possible within the scope of U.S. law?
Any businesses that takes payment in advance can use that money as they see fit, there is nothing special about insurance companies. Airlines, travel agents and construction companies are all examples of businesses that routinely take deposits.
What you describe is actually a common business model: it’s called “banking”. Banks take deposits and invest the money (usually through loans).
There are some businesses that are required by law to hold funds in trust but these are the exceptions rather than the rule.