Keith - it is more complex than that - mind you your quoted figure is less than NI with employee contributions of 12% and 13.8% employer. Here is a Wiki link that explains a lot more.
http://en.wikipedia.org/wiki/Health_in_Germany You will note the 'cap' on cost and protection for the low paid in place. Incidentally a cost of over 15% is quoted by Wiki not 14%.
The fact is you cannot compare the costs of two very tax systems and healthcare systems in that fashion. Clearly the objective is less cost, though the insurance based model should help with that overall and for individual costs too where any saving made by the government should be passed on in tax cuts. The real objective is better healthcare.
The principals of the German system are sound but I can see where a British version could be better but I will not go into that now.;
Tom - it would make a massive difference. When I had a problem a few years ago I got a referral to a private doctor and was subject to a whole range of expensive tests and all they found was high blood pressure but not a stone was left unturned to check just about everything possible. The point is the cost was not a concern for the doctor as it was not coming from a NHS budget but was paid for by an insurance company. It would have been a very different matter if it was NHS, a longer process because they would have had a concern about costs. In this case it didn't matter but if there was something more serious wrong then it may well have made a crucial difference to recovery.