It's not as absolute as you make it sound. Also because managing a team shouldn't require you to make very technical decisions. You should obviously know what you are managing but if there is a decision to be made, the people who spent hours on that subject will be your best experts and their guidance is essential.
In soccer coaches usually handle the strategic side of things and they have dedicated coaches who handle more player-related things. I think this is how a good manager in a normal company should work too. Make sure the team works as a team and take strategic decisions but not handle the nitty-gritty technical stuff.
But very few great (and I'd say probably even good) coaches never played at all.
Management, in the face of a stalemate, is going to address roadblocks from a human perspective. They will ask questions and listen. They will get people to talk and sort out their differences. Management will not weigh in with their own heavy handed technical decision unless they (and their team) has failed at the task of teamwork. Because no matter how good their technical chops, they are perpetually too far removed from the actual problem. Management will not really use the product the team is building. They can’t feel the impact of any one technical decision beyond how it impacts the team.
Technical leadership still has skin in the game. Leadership sets technical direction. They evaluate choices and tradeoffs based on technical merits. They are one of the resources management relies on. Leadership is going to have to live with the consequences of their decisions in their day to day work. They must use and build upon the thing they are leading.
Some people fill both roles. Some teams are lacking elements of one or both. Some teams fill these roles perfectly well in ad-hoc fashions, especially when you get teams of people strong in both areas - by far my favorite work experiences, everyone is exceptional and recognizes it in their peers. Then there is no hierarchy or need for it. That dynamic never lasts long, so we implement structures that try to capture it more broadly and often limp along for the sake of continuing to move forward as a group.
Is your company's core product a billing system? Then it pays to innovate on billing systems and differentiate from competitors.
Do you just need a billing system so you can collect money and move on with innovating where it actually matters? then buy and don't make.
wasting time on doing novel things that don't differentiate your business only puts you behind your competitors.
My experience has been that those who are too precious about the only role they've ever had (an "engineer") are difficult to manage precisely because of their inflexibility and lack of curiosity. It's ironic isn't it?
I wish this was more common but every time I had a manager without an engineering background or one who was a weak engineer, the ride was not smooth to put it kindly.
They don't need to be software engineers but they should have an overview of the industry.