I think that it would be important to answer the following questions.

* Who comes up with the "thoughtful questions"? And are they new every week?
* Who is responsible for the answering of these questions?
* What is the pace of the start-up?
* Will every team's concerns / progress / roadblocks / setbacks be relevant to management?
* How much time should each team spend on developing its response (related to point 2)?
* "...help employees feel heard, ..." - How do you plan to measure this?
* Is a weekly cadence the right pace?
** Can teams align their "wrap-up" with their natural development cycles (this is more relevant if the company is a technology company)?
* Will these wrap-ups be relevant to other teams?

Answering these questions can help develop how relevant these emails are both to employees and to management.