And even less people will want to create a mobilize account just to give you feedback. It cuts both ways.
Personally I just make it easy for people to contact me the way they want (https://blog.kowalczyk.info/contactme.html), I make it clear that I invite feedback and for my product I have a Discourse forum (https://forum.sumatrapdfreader.org/).
I don’t care about “private” part but I think discourse could be configured that way.
I wouldn’t over-think it (perfect being enemy of good) and I also wouldn’t assume that people really want e-mail blasts from you.
I also wouldn’t expect great engagement. My guess-estimate is that the ratio of “users” to “users willing and capable of giving meaningful feedback” is at least 1/100, so unless you have thousands of users, don’t expect much in the way of the feedback and even less in way of meaningful feedback.