I have been an individual contributor at large corporations for more than 10 years. Every time I have had a colleague promoted to manager, they always planned to stay technical and keep coding. Every one of them, without fail, stopped coding because they were too busy.
Thinking back to my managers who left for other roles, only one quit to work in higher management, the rest all went back to working as developers.
I worked at giant, globally distributed companies (15-25k employees), so I imagine that my experience is not typical.
I’ve been promoted into management for over one year now, and I’ve barely programmed on the job. I find it hard to keep up with the details on the application, but I still make an effort to with news, and do some programming for fun on my on.
I think it’s important for manager to still be able to make small contributions to the application. The manager isn’t going to own a big new feature that takes several sprints to complete, but he can still debug or solve some bugs, or make smaller changes. He should also have an overview of the code’s structure, and know about the technologies used to build the project.