Earlier quoted context omitted.
> "Our customers prefer the product works over getting a new feature, so let's ensure that at any cost" Do they, though? If a competitor launches a feature that all your customers want and start to switch to benefit from it, what are you going to do? Show burn-down charts of your bug backlog?
False dichotomy. The point of the quote is to worry about not breaking the product. It's still possible to deliver features while keeping it working.
Not really. This is the fact of real world software development: your resources are limited, and either you invest them creating value for customers so that they choose your product over your competitor's or they choose your competitor's instead.
If you spend your resources on technical debt and clearing bug backlogs even of obscure nonblocking bugs, you're just spending your resources to offer your users more of the same. If you instead use your resources to deliver new features that might have a nonblocking bug here or there, you're improving your position over the competitor's.
Time to market matters. A lot. There is no such thing as time to empty backlog.