That's absurd. Closing those issues doesn't make them go away, it just causes you to forget them (until someone else reports them again and someone creates a new issue, losing all the previous context). If you just leave them open, some will eventually get fixed, many will not, and that's fine.

The decision between feature work vs. maintenance work in a company is driven by business needs, not by the number of bugs open in the issue tracker. If anything, keeping real bugs open helps business leaders actually determine their business needs more effectively. Closing them unfixed is the equivalent of putting your head in the sand.