Customers (and customer teams) are a non-stop firehose of feature requests. It's important for the product team to hear all these requests, mostly so they can be understood. It's tedious work, but I do it with the intention of looking for patterns and having a pulse on the customers. You might be surprised by what you find, especially how many feature requests are actually different solutions to 1 larger problem.
My team does this using ProductBoard (https://www.productboard.com/) to synthesize all incoming feature requests on a weekly basis. We sit for 30 minutes as a team to go through direct requests, lost sales opps, etc.. This weekly work pays dividends when it comes time to prioritize features for the next quarter/year, etc.
Customer teams can feel empowered when they are given the tools/opportunity to prioritize things on their own, but the huge downside is that they feel silenced on a large majority of things they can't tell you (i.e. the "lower" priority" requests). This can really eat away at the morale of customer teams that feel they can't share their customer stories with you. When they hear feature requests from customers that they know are low-priority, it feels horrible to tell a customer it won't even be looked at by Product (it's even worse to lie).
I'd recommend a system where all feedback is shared, but only 2-4 feature requests are "voted" for officially by each customer-facing team.