An unused sword rusts in its sheathe.
I remember working for a gent years ago, who was stressed out that my output was so low. He declared "I started this business in my living room let me show you I can do any job in this building"
He came to my workspace, where I had 20 servers stacked on my workbench. He looked at them. Attached a single power cord. And then wandered off telling me he could definitely do the work if he wanted to.
I dont think a manager of software engineers needs to code the application he manages, but he should be continually coding something to remain sharp.
TBH one of my current clients produces hardware and software, medium to large enterprise with close to 200 staff. Their CEO can operate all their products, operate the machines that place chips on the circuit boards, operate the injection moulding machines, write SQL queries to pull data out of their CRM and write code. He tries his best not to do it, but he maintains the skills. That's the goal I reckon. Someone who understands the job all the way to the top.