I can understand why GP suggested company pays $20.
In technical support, one of the largest problems you have to deal with is all of the idiots that don't know how to use the product and won't look up the documentation or learn the product on their own. These people spam the shit out of support all day for the most basic shit. Seriously, I was working support at an anti-virus company and 85% of the calls into the paid business tier support were requests for us to do installs or basic application configuration for them. I know that not everybody knows how to configure a firewall, but "where do I download the install file for x" is literally Google-able.
The idea of an ombudsman is ultimately a bad one in this case because the problem isn't with the product or the support or the documentation. The problem is people Always think their issue is special and the most capable person should help them. Our support tier was paid, so more often than not we did what they asked, but the free customers would just get routed to a sales rep because free customers are even dumber and more entitled than the paying ones.
This whole situation is farcicle to me. Yet another free customer blew a minor issue out of proportion and had to apologize when it turned out the system hadn't failed him, he was just a free loading mooch all along.
Assume the company has no way of distinguishing "valid" or "high impact" cases from other cases. This means that in order for the company to handle cases they need the sum of fully treating every case to be greater than the sum of the cost of fully treating every case. This is almost certainly never going to be true, unless each of your cases is high cost to ignore (think enterprise support).
So you need to funnel down the cases. Typically this is done with low tier support that tries to suggest fixes and such. You can also offer high value added support to give customers the ability to pay for a support plan. This $20 proposal is like that but on a more ad-hoc basis.
Simplifying, that's "if (false)", since ignoring the customers in the limit gets you a failed business and bankruptcy.
And even if it is just a sufficiently large company, if the customer is not a large payer and the issue is non-trivial to solve, the the cost of losing that customer could very well be less than the cost of fixing the issue.
I agree that in theory you can accomplish the same thing by making the product foolproof, but I don't think you can accomplish that for consumer facing products, and that doing so may not be a worth while trade-off. Additionally focusing on issues that greatly impact people rather than small things that cause friction with the product may (or may not! if it causes lack of retention) be worth more.