Why is it, that when you seek a "free" service, e.g. www.mycleanpc.com they want a fee for doing what they adv?

Because the vast majority of these programs are, as you seem to have correctly deduced, bloody scams. It's probably a bad idea to use any program which claims in a banner ad to clean, speed up, or protect your computer -- and gods help you if the advertisement is a *pop-up*

In fact, it's almost certainly worse than a bad idea -- such programs are probably actively harmful, or at least annoying. My personal recommendation would be to look at Microsoft's list of at least marginally reputable anti-virus vendors[1], install the free package from one of those, and don't bother with spyware cleaners or disk Swiffers or what have you. The purported solution, in this case, tends to be worse than the disease.

[1] http://www.microsoft.com/windows/antivirus-partner...

Seems you're not reading the site correctly.

A free diagnosis is offered. A diagnosis is a report that tells you what problems there are with your computer. A diagnosis is far from being the same thing as a repair