I think this is a question of scale and hours in the day. In my experience when the team grows past 5 it gets difficult to do all the leadership things that “clear the road” for the team and also have enough focused time for effective programming. But at the same time, once you’re at that point, if you stop coding you can now handle another 5-10 direct reports. So you have to chose between keeping independent teams quite small with team leads who code, or with allowing bigger teams with a dedicated manager.

The scaling characteristics of those two patterns are different, because inter-team collaboration is pretty much always worse than intra-team, so the small teams are more effective if they are as independent as possible. If not you end up needing an extra manager to coordinate amongst the small teams... and now you have managers who don’t code.

The problem arises when you are evaluated based on your managerial responsibilities. The more time spent writing code, the less time you have to manage others.

If they wanted you to build things, they probably wouldn't have put you in management in the first place.