There is a major difference between "knowing something" and having it ingrained in your thinking process so it happens seamlessly.
You don't need this to be an engineering manager, but you need this to be a good engineering manager. Knowing and dealing with your own (and other people's) biases, understanding how power works in organizations, how different pieces of an organization interact and how the products you are building impact the financials of the company are basic requirements (but not enough) to be a good engineering manager.
As for the power dynamics stuff, firms in other professional fields do it all the time, and they don't seem to care about MBAs at all.
Lastly, a lot can be learnt on the job too. Maybe, statistically, engineers are more unlikely to show interest in this stuff, and that makes an MBA a "signal" that this person is interested in management.
It's a bloody expensive signal though, and it just saddens me that my career options and advancement might be limited because of it.
If by "technical skills" you mean "being able do to math", you're as far away from finance as "pressing keys on the keyboard" is from "coding".
You don't need a degree to be an engineer, and you don't need a degree to be in "management". But that's not the point.