I'm 20 years removed from any deep technical work at this point but I'm quite thankful that my CS degree's philosophy was that by the end of the program, you should be able to sketch out conceptually what's happening on a computer from electrons on a wire to how users react to your UI (basically, Nand2Tetris before Nand2Tetris). I've forgotten the fine details but that conceptual stack still exists in my head and it's an asset I'll always have.
There absolutely are many amazing managers of tech teams that are deeply non-technical and rely on their mastery of the abstraction layers they can grok to drive effective team performance. But there's also many times where the details do matter and the ability to dive deep into the guts of minutiae is an enormously valuable tool in your toolbelt. Management is a diverse set of skills and every manager rolls a different set of attributes on your character sheet and nobody is a 10 across the board. The art of management is to figure out what differentiated management style works with your character stats and build a team/environments to buff your strengths and make up for your weaknesses.
But the kind of technical knowledge you get from a solid CS education is too time inefficient to learn on the job and so there's real value to in absorbing it as much as you can in an collegiate setting.