"Also, if one customer is having a particularly bad time we need to be able to disable the feature for them while continuing to collect feedback from everyone else."
Exactly! And now feature X and the feature flag that governs it is in your code base forever.
In my opinion this all gets back to the way we build product and the expectations we have for our product managers. I have no doubt that their jobs are difficult in many ways, but the lack of actual focus on product specifically as it relates to customer sentiment always strikes me as lazy especially when that data collection is basically passed off to the engineers.