Just because nobody else is defending them (I hate phone robots too), I figure I have to play devil's advocate.

Remember years ago when you'd be put on hold for up to six hours at a time? That's because over the years, customer service phone lines have become increasingly overburdened with a growing volume of customer calls. In order to take some of this burden off of the operators, and to make the time you wait on hold shorter, the phone robots were put in place to more efficently direct customers to the appropriate departments without first having to wait for the main line operators to answer the phone. The phone robots are also there to deal with some of the questions most frequently asked (such as business operating hours, location, etc). This practice has freed up customer service phone lines enough now to make it possible for the operators to deal with situations that are more complicated (like the ones you have) without having to put the person on hold for hours at a time.

Meanwhile, the reason you have to sit through sixteen different options rather than being given the option to transfer to an operator at any time is because there are those people who would rather hear what the business's operating hours are from a live person than listen to the automated machine. That's why they don't tell you how to reach the operator until you've been through all of the previous options, because they're trying to free up the lines for people with legitimate questions.

Now that's in defense of the phone robots. What I really hate about phone robots (as in I killed everyone at the local Quik-E-Mart one time because of it) is the fact that many of them send you through this process, make you listen to all sixteen different options, none of them apply to you, and they don't give you the option to speak to an operator! AAAHHHH!