Usually when customers give feedback it's to address an immediate need they have, so they'll suggest adding a button/option/toggle/whatever. And that's fine, but if you do that for every piece of feedback, you'll end up with an unusable mess. Especially because it's usually very easy to add that one extra button/option/toggle.
You usually require someone to go through all the feedback and try to address the root cause of what they're asking for. Sometimes the extra option is unavoidable, sometimes it leads to redesigning some system to be more generic to support what the customer wants + more.
I do think the feedback needs to be linked to the work somehow, not hidden away in a separate PM tool or whatever. Ideally retaining the raw feedback, because sometimes when summarizing it, things get lost.