Wow, that's an insane request for a director. Even at the management level, unless you have a specific, obvious "dual role", this borders on inappropriate.

The company in the first case was the closest to correct. If you really weren't sacrificing your commitments, then they're being unreasonable, but I can say I understand their perspective.

So many engineers move to management, yet want to remain "hands on", and won't let go. It's obnoxious and frustrating, when they inevitably have their heads spinning from meeting after meeting, and no time remaining, but still insist on trying to help.

Simply looking at code output and calling it a problem to produce too much is hilariously shortsighted, but I can see how someone with some bad experiences could trend in that direction.