Harry Potter's world

The Harry Potter books suffer from a "big picture" problem. There seems to be a large population of wizards, some who live in their own town (Hogsmeade), though most live in mixed-Muggle/Wizard places. How do these wizards earn a living? They can't create food from nothing (a rule arbitrarily introduced in the last book), and there is such a thing as wizard poverty, so there must be wizard farmers and labourers somewhere. But what do all the other wizards do? Most of the wizards whose occupations are known are working in service industries:

Bill Weasley works at the bank.
Percy and Arthur (and many other characters) work for the government.
Many wizards work in education.
Some wizards work in stores, but it seems that those that do also manufacture their own goods; Ollivander makes his own wands; Fred and George make their own Wheezes, etc.
Harry and Ron want to be Aurors, i.e. police. Do wizards pay taxes to support the police?

Also it seems that even as the young wizards approach their final years of school they have nowhere near the skills of the teachers in the school. Even Harry never wins through magical skill; in fact his talents seem negligible compared to Dumbledore, who can walk into a cave and determine what spells were performed there years ago.  This suggests that there must be a higher education institute somewhere where they can learn more applied magic, but it is never mentioned, and in fact quitting school to strike out on your own is perfectly acceptable.

Finally the wizard community is remarkably aloof and isolationist when it comes to the Muggles. They can never understand anything non-magical, not even the money, though basic math should fix that... oh wait, they don't study math at Hogwarts. In fact they don't study anything mundane. But surely someone who can understand how to run a household or investigate a crime or make change in Galleons and Sickles should be able to understand how to use a telephone after a try or two. But there seems to be some kind of mental block that applies to all the characters not raised by Muggles.  This suggests that muggledom is akin to a language, in that you can learn the muggle way as a child but not easily as an adult.

It's possible that by raising these objections I'm missing the point, which is that these are kids books about a group of friends growing up in a tough world.  But I feel that a more thorough approach to this issue would have made these books remarkable.  Instead they have an inconsistent world where many of the characters show signs of insanity or incompetence and the world's limitations are numerous and arbitrary.