Consolidating feedback is a problem for any team at scale regardless of who is doing the support. Dedicated customer service teams have a more complete view of what's going on with customers, than the average rotated employee, but at the same time both need a way to bubble up that feedback to the product team.
More importantly, it's essential to understand the difference between the problem you head about today, verses the problem that customers have been facing for a long time. (I do think that support rotations cause a bit of a recency affect in prioritization for better or worse)
In the long run my argument is the closer you are to your customers the better insight you'll have in general. Because we all make a ton of decisions that aren't clearly specified, and we want everyone on the team to have the best intuition for the customer when they make those decisions.
More importantly, it's essential to understand the difference between the problem you head about today, verses the problem that customers have been facing for a long time. (I do think that support rotations cause a bit of a recency affect in prioritization for better or worse)
In the long run my argument is the closer you are to your customers the better insight you'll have in general. Because we all make a ton of decisions that aren't clearly specified, and we want everyone on the team to have the best intuition for the customer when they make those decisions.