Our support team is not technical in any way (they are support for our entire moderately sized membership-based nonprofit), but they are consistently a source of extremely high quality feedback, for the reasons you mentioned.

If there are serious UX issues, your designer might not uncover them, but support will hear about it. If there are edge case performance issues, your dev team might not uncover them but support will hear about it. Very few people know more about how real users interact with your products than support.