I like the idea of this, but why not just have some time per week/sprint for bugs? At my company we prioritise features, but we also take some bug tickets every sprint (sometimes loads of bug tickets if there aren't many new features ready for dev), and generally one engineer is on "prod support" which means tackling bugs as they get reported

Because marginal work is only marginally rewarded. Spending one week and coming back to whoever with a nice piece of paper saying we fixed 60 bugs will earn a lot more rope from non-technical folk than fixing 3 bugs per week - the latter just looks like cleaning up your incompetence.