If you ask for feedback, and you receive it, and then you don't act on it... then why bother at all?
This is available on a personal level as well as a business one.
If you ask me to spend time sending you some feedback (through NPS or otherwise) and then nothing really happens -- more often than not I get annoyed.
So please, don't ignore #customerfeedback. It will also improve your product or service in the long run, so it's a win-win situation.
And if you struggle with a huge backlog, there are ways to deal with that as well.
Reach out if you have questions - I'm open to technical and non-technical discussions.