All things equal, I would prefer a single payer system.  But single payer won't make doctors any better, nor will it reward those who make the correct diagnosis the first time.  No matter who is paying, whether it be private insurers, the government, or some combination, the incentive is to provide more services, not the proper services.  Medicare has the same problem in this regard as the private insurers.  I just spent the winter in hospitals with my dad for a heart attack, three hip replacements, two infectioins, etc, and my dad's experience (with medicare + a medigap policy) was roughly the same as yours-- missed diagnoses at several points, delays in surgeries, seemingly unnecessary extra procedutes, and so forth. There were a lot of great nurses and doctors, but it seemed like there wasn't a lot of coordination.  And, from looking at the medical statements, it is just all ridiculously costly.

By the way, the only reason my dad had ANY of these health problems?  The shaft of his original hip prosthesis broke in his femur.  Likely a defective product, perhaps used because of a physician kickback (we did not investigate or sue but there have been big class actions on defective hip replacement joints, and I do not understand how how a solid steel/titanium shaft can just break in half).  He had the heart attack just after his hip revision, and that led to all the other problems-- including a hospital-acquired infection in the other hip (also an artificial joint), which had to be replaced twice, weeks apart, in two more arduous surgeries and recoveries.  Before this, he was a healthy and active 80 year old man.  Now, he's just trying to get to where he can walk without a walker and drive again.

My plan is to just never get sick...