I have a friend who runs a division at an engineering / mechanical / aerospace firm. Decent size - about 5000 employees.
They will never hire a graduate from an Ivy League or top school. Same reasons you mentioned, but also: difficult to retain, they resent what they might consider "drudge" work or unsexy projects, especially as a new hire, and resist being formed to the culture of the company.
His view is - let 'em go fight for jobs at Google and Amazon.
I worked with them at a high tech IT company and I won’t hire a Harvard grad. MIT or RPI or Northeastern is another story