No, not just that, there are now specific rules to place those without hukou ahead of those who have. e.g. in my area, say kid's dad has hukou in the local are

No, not just that, there are now specific rules to place those without hukou ahead of those who have. e.g. in my area, say kid's dad has hukou in the local area and kid's mum has hukou from another area in Shanghai, then the kid will get lower priority for applying schools in the area comparing to those with one of the parents with hukou in the area and another one without hukou in Shanghai at all. The logic is that the first couple has the option to send their child to a different area in Shanghai while the second one doesn't have such option available to them.