In the positive side the proximity to schools is very convenient if you have kids and those kids have activities at the school (obviously). At different times of the day the area is quieter and if the home backs up to the school when school is out you have no rear neighbors. If you like kids the sounds of children playing is hardly a concern.
Conversely schools do impact neighborhood with people and auto traffic and the related noises of school activities and events.
As you see the plusses and minuses are the same, it all depends on you and your preferences.
With prices going up the people the probability that the school is the issue for movers can not be attributed directly to the school.
Typically what happens is someone puts their house on the market and neighbors realize they can in this market get money money that they thought. So what happens is neighbors want to sell their homes.
I think being near the High School is not the reason why they are selling, it some ways it is a benefit. Children can walk to and from school and the don't need a car. It can be busy when school starts and finishes but other than that it is the same a s buying a home anywhere else.
It a personal choice for you and your family.
My son attended a large secondary (grades 7-12) school, and the houses close by carry a distinct premium, just for that reason.
And if kids attend after-school activities, they can walk home, rather than relying on parents or sporadic, limited bus service.
As for disadvantages: If a large number of kids drive to school, or the school's population requires many school buses, then the neighborhood can get VERY congested around opening and closing time. Where my son went, that peak period lasted about 30 minutes. Luckily, there were plenty of other routes around there if the goal was to drive from one side to the other. But that can be a problem.
I suppose, also, that the noise from the various fields (soccer, football, baseball) could be irritating, not only on game day but during practices.
And, finally, if the school has gangs, there might be gang activity around the school. (Wasn't a problem where my son went.)
One thing I'd suggest: Contact some of the people who'd be your neighbors. Ask them whether they consider the close proximity an advantage or disadvantage.
Hope that helps.