I have long had an idea that the best way to handle this is a community supported prioritization service.

In other words, a community (hacker news, some subreddit, or perhaps an independent site) would invite people to post problems that ought to be easily solved by customer support except that the company is failing at customer support. Because problems tend to repeat themselves, the people who spend time on this forum would be able to identify (and sometimes provide workarounds for) the majority of cases -- all at no cost to the company that was failing at customer support.

The remaining cases could be ranked by the community according to how egregious they were. Then the company that was failing at customer support could assign a tiny amount of actual attention to look at just the top few issues sorted by the community.