I work for an insurance company, and it's possible that they might reimburse you for the time you spent, but it depends on the insurance company and it depends on how you substantiate the value of your time. For example, if you are an hourly worker, and you can prove that you missed time off work, then it would be easy to come up with a value. You can also do this if you earn a salary, just do the math. If you didn't actually miss work I don't see them paying you just for your otherwise "free" time. That's getting a little ridiculous. Shit happens, don't get worked up over a couple hours, life is too short. We have paid for claims that included payment for people's time, but were talking about taking full days off work to take care of issues related to the loss, not a couple hours of shopping.
I understand where you are coming from, but it's not just two hours shopping. It's two hours spent doing something he doesn't want to do that is taking up his free time because of someone else's negligence. And that two hours could have been spent doing something he actually wanted to do, but now can't. PLUS, he has the actual labor of physically installing a new mailbox.
I think a couple hundred bucks on top of the actual cost of the mailbox, is extremely reasonable.