Socialized Medicine - What's it like?

I’m bumping this thread, because I just read an article contradicting a statement I made (here, and in many other earlier threads on this topic).
I stated that the “waiting list” phenomenon was most likely caused by an underfundinc of the public healthcare system, since it happened in some countries but not in others.

But the brief article proposes another explanation making a lot of sense. The waiting list issue is correlated to lower healthcare expenses, but not caused by it. They’re are both consequences of two different ways of organizing the public HS.
In system A, in France for instance, the patient can see any doctor he wants and get an appointement with any specialist he wants. The doctors are remunerated on the basis of the number of medical acts. So, if a patient visits his GP ten times, the GP gets ten times more money.

In system B, in the UK for instance; the patient register with a specific GP, and must be refered to a specialist by his GP (if he wants to receive medical care free of charge, that is). The doctors are paid on the basis of the number of patient registering with them. So, if a patient visits his GP ten times, the GP is paid the same.
System B somewhat restricts the patient free access to medical care, and also provides not much incentive for doctors to often see their patients or to undertake many medical acts (which might be a good or a bad thing, depending on whether they’re necessary or not) like in system A , but an incentive to see as many different patients as possible (so reducing the number of doctors needed). Both have an interest in keeping their patients, though, of course.
So, system B tends to result in both longer waiting time for appointments (medical care providers aren’t in a hurry to see you since it won’t change their income anyway, as long as you won’t be pissed off enough to search for another provider), but also in lower medical expenses.
I’m not saying that this is a definitive explanation, but at least an interesting and sensible one.