The problem is Google is trying to approach other industries the same way they have with Search: If it can't be solved by a group of engineers and a rack-full of servers, it shouldn't be solved.
Is that a problem, though? If people in a particular market segment value high quality low cost services over accessible customer support, the strategy succeeds. If customers in that market segment value accessible customer service enough to pay extra for it, it fails when another competitor comes in to provide that and takes all the customers.
But what Google is providing seems to be what most customers want most of the time: People bitch about bad customer service when something goes wrong, but they still choose the free service over the paid one pretty much knowing that that will be the case going in.
The market decided that what Google is doing is what people prefer. The general population could have a change of heart and decide to start patronizing companies with better customer service who charge correspondingly more, but they probably won't.
It's a problem to the OP, and it's a problem to a lot of users who suddenly lose access to their GMail accounts and don't have the luxury of getting to the front page of HN. Just because it's not a problem for 95% of people doesn't mean it's not a problem.
I'd also argue that most people aren't aware Google doesn't have customer support going in. Did you explain to every person you recommended GMail to, if you've recommend it to anyone, that there isn't any customer service should they get locked out of the only email account they might be using for the next few years? You might be a smart hacker and know to back up your mail on multiple drives each night, but most folks assume good faith about a company they deal with.
It's not a problem for 99+% of people. That means it's not a problem for 99+% of people. It's like any rare but unfortunate event that people rationally choose not to insure against. And it sucks to be you if you're the statistical outlier, but you already know what to do if you're worried about that: Choose a different service that has a worse overall user experience because they spent their money on giving you someone to talk to on the phone instead of on producing a well-engineered service.
All this time I've given Google no money at all.
It goes somewhat like this:
If you paying money, you might have luck getting a phone support based on your investment. However, if you are on the other end of receiving money, good luck having someone respond to your email or on the forums.
I shot a mail address using a contact form and in less than 24 hours I got a phone call which solved all my issues in that same call.
I've been locked out of my AdSense account for breaking the TOS, but they won't tell me which point of the TOS I've broken (which, as far as I can tell, was none) and the only way to get around this was just to create a different AdSense account. Which is against their TOS BTW.
That interaction with Apple was not the first not last, but the only related with an online service. They've fixed hardware, dealt with recalls and even took care of stuff outside warranty.