It is necessary for team members to be exposed to some amount of customer feedback, with the level of exposure being decided by the managers of the team; as well as the number of members of the team who are exposed to such feedback.
An important question is about why the team members need to be exposed to customer feedback; after all, in the classical definition of the processes of the team, the product manager is the one who is exposed to customer feedback, massages it to the appropriate functional change or addition and then puts this to the team in terms of the prioritization of this feature vs. other features; or classifies this as a defect which needs to be fixed, again as per prioritization.
However, the classical model needs to be changed. I have seen how exposure to customer feedback changes the way that the team works, their responses to defects, and the eagerness in some of the team members to get more involved with some amount of customer interaction. The biggest advantage comes in terms of getting more acquainted with the customer mind. In some cases, the shock when the team members realize that a defect that they had ignored as minor got some customers really hassled. In one case, the defect was raised to the company management through outside means and came down to the development team as a must fix; when the product manager saw the defect, there was some amount of discussion because this was a defect that had been raised earlier but had been dismissed since it was deemed as too minor and even more surprising, not really impacting customer workflows.
Even senior engineers on the development team have seen jarring signals, whereby the features they worked hard on and pushed a lot, were not really seen as important by the customer while the changes in some of the workflows that was prioritized as higher by the product management was appreciated in customer feedback mechanisms. What this did was ensured that the senior members of the team understood that they need to setup a regular structure of how to get customer workflow, as well as listen more to the product managers. This is even more important when you have development team members who have been there for a long time while there have been changes in the product management team.
Another advantage of getting customer feedback through some kind of mechanism is that the team will also get more acquainted with the people who actually interact with the customers, whether this be the customer support team or some similar kind of support mechanism, and this kind of interaction helps the team do question and answer where they learn even more of the kind of common problems that customers have in terms of workflows, and makes them more receptive to requests for changes in workflow rather than introducing new features.