If they didn't deny the claim (or lose it) in the first place they wouldn't have to communicate with us at all.
The insurance companies probably spend more money trying
not to pay the claim than they would by just paying the stupid thing. They have strict timely filing limitations so if you submit a claim and find out they "just don't have it" but it is 60 days after the service was rendered, you are s.o.l. as you cannot get payment now. And no, you cannot bill the patient either. Think of how much money they are saving with all the physicians who do not have vigilant billing staff and let these time frames lapse.
Much of what we do is also for the patient's benefit - it is easier to get the money from the insurance company than it is to get it from the patient. We are customer service oriented. We want the patients to be happy with us so we spend the majority of our time being the middleman between the patient and their insurance company and leaning on the insurance company to pay.