I'm all for fewer (and smaller) meetings, but there is a time and place for synchronous communication. Especially quick informal communication can be incredibly high leverage. Optimizing for heads down time is great if everyone knows exactly what they should be heads down on and thinks the same way, but that is not always the case.

If you call yourself a manager--which is a questionable role at startups--then you need to be optimizing for the entire output of the team. Rigidly declaring everything must be async text is no better than scrum by numbers.