What I would say is that it's possible but very rare to do this well, and furthermore that people often don't have an accurate sense of how well they're doing at it. The individuals on the team might know but might not want to say, but an even bigger problem is the individuals on the team not being aware there is a better way. I was about a decade into my career before I had an experienced dedicated engineering manager. I had already spent time as a tech lead / manager myself by then, and thought I had done ok, but experiencing a dedicated engineering manager made me see that I had actually done the job quite poorly.

You may be doing it extremely well! It does happen. But I can understand why you're getting skepticism.