How important is it for a coach to stay in shape as a player?

TLDR: How important is it for a coach to stay in shape as a player? And what practices help to this end other than staying active as a player? One method is to revise their material and/or syllabus more than re-using existing material or the material they used previously. Any other ideas?

Recently, I saw an article/post online talking about how a chess coach who is not active as a chess player drops in playing strength, essentially leading to a 'convergence' of strength of teacher and students over time. Even in cases where a coach wants to stay active as a player, the time spent could be more on improvement of students than their own (e.g., they could be analyzing student's games more, and reviewing their openings more). So, my questions are   
1. For a coach, how important is staying current as a player? 
2. What practices help to this end other than staying active as a player?

I believe this 'convergence' phenomenon is not specific to chess. In any discipline where the knowledge-base is at least as important as skill, this type of phenomenon could occur. For instance, it is less of an issue in physical sports, since the coach need to stay updated about the strategies, but need not have or keep up the skill required to execute it. One example where it is highly relevant is school/college education. There, one method teachers usually employ to staying current is to revise their material and/or syllabus more than re-using existing material or the material they used previously. This is definitely useful for chess coaches as well.

Other than this, is there any technique that helps a chess coach to staying current as a player?   
I would love to hear if you have some ideas in this direction (please post your ideas as comment, or provide link to them in comments). Thank you. 

Two related Wikipedia pages: Dreyfus model of skill acquisition, Reflective practice