I work in IT. I've actually managed a servicedesk, so an opinion from the other side as it were.
The purpose of the first line call handlers is to keep people from wasting the time of the 2nd line engineers by eliminating the spurious issues, like people calling saying their computer isn't working, only to discover either it's not turned on, or there is a power cut. (and a lot of misc training issues as above!)
Yes, people really do call in with things like that daily. The percentage of real technical issues is actually under 20%. Fighting the system is pretty pointless, since the people who fight it the most honestly are often those we need to keep away from the second and third line staff to let them get some productive work done.
Given that I have to deal with other servicedesks semi regually (that's how you get parts etc) I can fully appreciate the issues people have when you actually have an issue on a bad servicedesk because i've had more than my fair share. (Dell's helldesk is really awful, though the HP one is quite good. They aren't locked to the script)
Basically, if after you have explained what the problem is and the person is still refusing to deviate from their script then they won't do at all, and the quickest and most painless way of dealing with them is simply to allow them to work through their script until it gets to the "escalation to somebody competent" bit. This should take under 5 minutes on average, because the script writer wrote the script with the intention of letting the helldesk tech move onto the next caller quickly. While I would occasionally like to extend my arm down the phone line and choke the person on the other end, getting irate at them only means you spend more time speaking to them because they can't complete their script.
Telephone calls always get logged, but it's actually quite difficult to log the relevant details of the problem since it's rarely apparent exactly what the problem is, and when users do give you all of the information it's usually contained within a torrent of useless info. The chances of the right info getting written down is shall we say slim since if your lucky about a tenth of what was said will be logged and it's rarely the right tenth. In a real servicedesk, the good staff get moved up to second line or first line management quickly. Who do you think that leaves taking your calls?
The second & third line guys were constantly complaining at calls not having enough details logged. If you want to get a decent response, send an email detailing everything you've tried. First line will probably still have a good go at seeing if they can lose you anyway (they do have targets for resolving a certain percentage of issues, and they'll ditch you if they can get away with it) however you can call in response to their email, and even if you have to work through the entire script then that email will get logged into the system, and when the first line guys give up and pass it to second line (someone competent who's not working from a script!) then they actually have all of the information down in front of them and can probably give you a solution strait off.