Also, ostensible insurance coverage gets you through the door and the treatment needed without taking all of your money. Cash patients often have to pay large chunks up-front.
As a person in a fluctuating employment situation with a pregnant wife, I know that cash OB/GYN pregnancy treatment programs cost $400-$500/mo, because they want you to prepay on the baby's delivery, as they don't trust cash patients to pay a $12,000 bill after the baby is born. If you have insurance, at the two ob/gyns we've been to, you don't even have to pay office copays and they bill it all after the delivery. The individual is usually billed $2000-$4000 after deductible and after the insurance pays its portion (generally 80%).
So, even if your insurer denies your claim, for some people the only practical way to get access to medicine is to have an insurer. Certain doctors (namely doctors with whom you will have a short-term ongoing relationship, like your infant's pediatrician or your OB/GYN) will totally shun you if you don't have insurance. I guess this is because most cash patients determine they've paid enough after they pay a pediatrician or gynecologist several thousand dollars.