My kids are not a part of the hukou system. The whole thing, imo, is much more trouble than it is worth, especially if you're only going to be here for a few years. Kindergarten is no problem with or without a hukou, it is only grade school, so you have 6 years, at the very least, before school becomes an issue. They are changing laws regarding foreigners and public school too -- schools are technically required to accept foreigners now, and the fees are high but not so high that they're anything a family raising a kid couldn't afford. Nowhere near international school fees. Most people who are into discussing this sort of thing also give the hukou system 10 years max before it is done away with altogether.
As a foreign woman giving birth I was never ever required to produce permission to have a child. Your wife, if she's working for a government danwei, may have some trouble on the official end of things, but otherwise it should not be an issue.
The problem most foreigners have with local schools is not the access to them -- it is fairly easy to, if push comes to shove, bribe your way into a school, whether you're foreign or not.
The consensus seems to be that the benefits of a foreign citizenship (from the "right" countries) far outweigh the benefits of Chinese citizenship. In China you're not allowed to have 2 citizenships. Some people fly under the radar but technically your kid could have his hukou taken away anyhow for being a foreign citizen. All the hoops you jump through to get this kid official in China could come to nothing. Apparently having your child have a hukou also makes it a bigger hassle when you want to take him out of the country. I believe one of our regulars -- maybe Raoul even -- had some experience with this at some point.
If you're planning on staying in China for life your kids would probably want to be official, but I don't know a whole lot of foreigners who, after having children here, still firmly want to stay in this country forever and ever.