One of the ways of ensuring that the process remains ongoing, that the team does not get tired of seeing these problems with customers in their workflows (from experience, it has been that direct ongoing interaction with customer support to get information about problems can get depressing to the team, just hearing about problems and more problems), that there is a controlled system of working this feedback into the schedule of the team members. Managers of these software teams do get involved, but it cannot be a manager driven, command ruled interaction with the customer support team.
One way of ensuring that the team remains involved with the customer issues, including with the customer support team, in a controlled manner, is by deputizing somebody from the team to handle this interaction and figure out the parameters by which the team would operate. The person who does this works with the customer interaction team (primarily the product support team in most cases), works out the schedule of such interaction, works out the prioritization of the issues that are thrown up about customer workflows, and tries to work out a system whereby problems are highlighted, as well as positive customer workflows feedback or any direct appreciation from the customers about the product or the development team directly (this needs to be genuine feedback, not something that is created to keep the team in good spirits; you would not believe how many times positive news is massaged to make the team happy).
This entire plan of what the person is expected to do, as well as a slight reduction in the work schedule of the person in order to give them time to handle this additional work of customer support interaction is something that would emphasize to the team the importance of this work. In addition, the managers should atleast have some critical items from the customer feedback that are meant for incorporation into the product, again emphasizing the importance of feedback from the customers. It would be ideal if the person who is appointed the champion gets some prioritized items and presents this to the team and the product manager.
The role of a champion for this effort is something that should be offered to the team, to any member of the team who wants to work on this. Even though the managers might have somebody in mind for this, they should let somebody else do this work unless the mismatch is too high. The position can be rotated at a regular interval, say maybe every quarter so that more people get exposure to this role and also more exposure to feedback from customers.