Waiting on hold

What is is with automated messages and systems when trying to call a doctor's office, a university, customer service or other such places?  I understand WHY they are there - there is not enough man power to answer the phones and even if there was, the chances that every single one of those people being able to answer just about any question that someone can ask is very small.
However, I have noticed that almost every time I call a company and have to go through one of the automated systems, I get put on hold (at some point during the call) for at LEAST 10 consecutive minutes.  For example, right now, I am trying to get a hold of my university and was on hold for precisely 19 minutes and 36 seconds before I got to speak to an actual person.
Why is it that companies and businesses let this kind of thing happen?  If you just need someone to answer the phone to lead to happier customers, patients, whoever, then why not hired 1 or 2 people JUST to answer the phones?  I know that may seem like a lot of people when you consider how many companies should do that but hey, it might fix the unemployment problem, right? Especially in areas like Tampa, where a university alone would have to hire probably close to 100 people to fix just that problem. Just imagine! But I digress.
My phone call lasted exact 24 minutes.  So, let's do the math, shall we? Out of 24 minutes, 19 and half were on hold, not even talking to someone.  Probably 30 seconds of that was pushing buttons so that I could get to the right avenue.  That means that for only 4 and a half minutes I was talking to someone.  In what world is that okay?
Okay, so maybe I'm being a brat about it, but it's just very obnoxious and when this kind of situation happens after an incident where you are furious about a service or product, it can seriously get on your nerves!  At least, it gets on mine.  Like when the gas company was taking double payment and no one bothered to fix it until I called them up.  And even then after that, I had to call back another time to make sure they were following up.  I remember that day I was on hold for about 10 minutes and my nerves were very thin.  Everything worked out with that and with today's call.  But, is it really necessary? Are offices really that busy on a Friday afternoon? I'm pretty sure most people who work in an office, by the time 2:00 PM hits, they just mess around until they can clock out.
Anyone else have any fun stories to share about being put on hold?