It is typically very hard for the parents when we change a school start time, sometimes even when the change is small.

Doing small changes can help, but it is so politically complicated to change the school times that some districts prefer to do it all at once.

Because done that way (in addition to what sibling comments suggest), halfway through, there'll be a point when everyone has to get to school at the same time and the bus fleet will have to triple, at huge cost. Or you just end up doing a large disruptive jump anyway to avoid that timing issue.

Of course they could, but as the article mentioned toward the end, the school district no longer has the political capital to pursue rearranging school schedules. The superintendent lost his job over this. I imagine votes were angry with the school board.

Repeated change has its own substantial costs for a system as large as a school district - even without the outrage over the drastic change, reworking schedules every year would be enormously unpopular.

(Think of everything from changing heating and AC schedules to reworking start times for bus drivers to telling parents they need to drop their kids off at a different time each year. There's a reason most school administrators I know get an absolutely hunted look when you mention changing anything.)