For an inkjet printer with paper feed issues pulling it through a few times might actually fix those - the print head should be far enough away from the paper that it will not get damaged, and there shouldn’t be other parts close enough. I’ve prolonged quite a few inkjet printers life in the 90s by just sanding the rollers a bit (in some cases you could even get maintenance kits from the manufacturers - which just would be an overpriced tiny piece of sandpaper).

In a laser printer I’d be worried about some of the internals, though.