This idea is very special because it will bring the administrator closer to the public and users directly.
I agree with everything you've written, but a "subforum" of suggestions could be made in the suggestions tab itself, so it would be a steerable link. The administrator sees everything but an approximation more visible and frequent would be very important, it would bring much more participation from the users.
This participation and response to suggestions could have a date in the week/month or something like that and thus eliminate the need to have full frequency.
GoogleForms is a simple and interesting option, but xat could develop its own feedback page similar to GoogleForms, thus bringing authenticity and innovation.
I look forward to this suggestion being well received by the team.