Feeling overwhelmed by insurmountable mountain of bugs and issues is not the way either. We can argue that closing the tickets is not the best way, but if realistically nobody will ever look at them, why not make the developers feel better.

Either you truly need to fix the bugs, in which case the feeling is good and maybe more effort should go that way (more resources assigned to it or whatever), or you're at a scale where tackling everything is impossible and you shouldn't feel overwhelmed by seeing the noise then.

But I think modern industry pretends all it's fine to convince themselves that it's ok to chase the next feature instead.

Because it isn’t about the developers feelings, it’s about the users. Why not set aside a day or half day a week to fix those bugs instead?

Move them to a deficated status. “Never triaged”, “lost”, “won’t do”, what have you.

That way, you’re at least not deluding yourself about your own capacity to triage and fix problems, and can hopefully search for and reopen issues that are resurfaced.