Blaming the "startup mentality" makes a good linkbait title, but Occam's razor suggests that when the latest cool-sounding attempt to reform public schools in cities fails, it's probably for the same reasons that previous cool-sounding attempts to reform public schools have failed: politics, turf wars, existing vested interests, and so on.
This, of course, is not really about the startup mentality, but about the mentality that sees nothing wrong with a kid's school being determined by a lottery instead of parents' choices.