I have a slightly different take on this. I think every company should dedicate a certain percentage of their revenue to handling bug reports from users. Yes, many bug reports will be bogus, but many will be pure gold (I speak from experience). Yes, it involves a lot of manual work. But it is so incredibly worth it — you get to catch the odd bugs that you will never catch with automated or in-house testing. In contra…
Usually Support is seen as a distraction to new product development or whatever the strategy is, but often I see management overestimate how much time and money is spent on it. So, just tracking that cost/time will likely increase it and improve customer satisfaction.
Unfortunately, improving Customer Support is not rewarded in organizations as much as cutting costs, creating new products or expanding revenue, so you'll probably need the CEO to care a lot about it to improve matters. And CEOs can't really put a number on improving customer support, so it is optimized to cost less over the near term, not deliver a better service.
I also see the worrying tendency to keep only Customer Service or equivalent responsible, as if they can fix the bugs and improve the design.