Sometimes, those questions reveal good answers. However, usually the answers are these:
"1) Why can't you put them through to support?"
I can. Support is backlogged. They'll be on hold with them. That's why they're ringing me, because they're angry about being on hold.
"2) Why is your support phone line so poor they can't even answer a phone, which is their one, primary and sole purpose?"
Either there are not enough support staff (not my responsibility if I'm answering another phone), some are sick, some other customer has a major problem and they're fixing it, it's a time of day where support has ended because we don't run 24 hour support but I'm working late, ...
"3) What do you expect users to do when they can't get through on the line they are supposed to? Write you a letter to solve their support problems?"
Per the answer to 1, I expect them to wait on hold. Then, perhaps, send a letter to the responsible party (I.E. the head of support or their superior) complaining about having to wait on hold. They should not complain about that to me, as that's not my job and I can't do anything about that.
"4) Why are your sales staff - when they get a call and can't get even through to support themselves - not able to have the most basic of support functions available to clear your sales lines for what THEY are intended for. Even if this is a limited checksheet, filing a ticket direct to support on the customer's behalf, etc.?"
Because sales is not support. You don't hire sales representatives for their ability to support customers, because that's not their job. If there is a convenient page that they can give you, that's always nice to have, but many users will either refuse to read it or have a problem that is more complex. In that case, it is not the job of sales to support the systems. I also don't expect that a customer that calls the HR department will get IT help.
By assaulting a sales office when support is bad, you are punishing the wrong people. The people responsible for the problem, assuming that there is a problem, are not the people answering the phones. Those people are trying to do their job, and you are preventing them from doing that without any good reason. As fun as your autodial story was in a BOFH way, it's not the right way to deal with the problem you faced.