It’s not about doing more than one thing at once, it’s about picking your battles. Leaders have a limited amount of what I call “credibility capital” (see https://jasonlefkowitz.net/2003/03/where_leaders_f_1/) they can use to get things done. The more of it you spend on issues unrelated to your core strategic concerns, the less you have available to spend on those.

Some leaders have tons of credibility capital banked away, so they can afford to freelance on the side. But freelancing is a luxury. Spend too much on that and you’ll fail at your main job.