Though MBAs have certainly been growing in popularity over the past few years.
It's not constant across the board, as there are plenty of IT companies that seem to be doing a decent job at promoting engineers. But then I read a lot of people here talking about "up or out" views of engineers who are above a certain age. It's complicated.
That makes sense to me actually, since you need to have a high level understanding of how businesses work and what stuff the C-suite needs to be doing in order to understand how to value a business.
The C-suite might be the one place where the "generic management skills" might actually be really useful. But middle management and day to day supervisory functions? You can't manage what you don't know, and if you don't understand the processes of the people you're managing you're blind.