As more and more housing is built, the supply level rises to meet the demand level, and prices level off and stabilize (and often drop).
Right now, there is an artifically low level of supply vis a vis the demand, because of rent control.
And no, you are probably not going to be paying as low as you would in any other city, but it will be lower overall eventually if rent control is scrapped.
There are many factors governing what out-of-towners are willing to pay for rent, also, such as going salaries, the state of the economy in general, and demographics (large graduating classes cause rentals to go up).
As for the schools: The situation is that NYC (and Washington) has an elite worker class, served by minorities. Because NY is a magnet city, the influx of very qualified college grads is constant. Why should an employer (absent federal laws, of course) hire a poorly prepared high school grad when she can hire an Ivy Leaguer? Thus the kids have nowhere to go but service jobs, to make sure the elite have their packages delivered, their tables bused, etc. Having nowhere to go tends to stifle incentive to do well in school. Even graduates of the city colleges (open admission until recently, with remedial classes) are poorly prepared in comparison with someone from New Trier High School.