That's not what it was at all.

Any time you say that something can't be done, you will attract people who say "I have found a way to do it!" Even more so if you have a proof that it can't be done. This phenomenon is far older than the internet; the term "morbus cyclometricus" suggests its origins in antiquity.

The FAQ maintainer was not looking to profit off fools. They wanted to chase them off; after spending several pages explaining why the task is impossible it is tedious to explain to a crank (the term generally used for such people, as described by Underwood Dudley) that they are in fact wrong, the task is impossible, and here's why. It's easier to say "Pay me if you want to waste me time" and reasonably assume that no one will do it.

It's similar in spirit to the James Randi challenge. You're not going to win it, because you're not going to prove that math or science is wrong. But the JREF had as its goal to expose the charlatans, and had the time and resources to devote to the task. A newsgroup FAQ maintainer has neither the time nor the resources. So they shouldn't have volunteered? Then you have no volunteers. Hooray for the internet.

Now yes, every once in a great while someone will come along and legitimately do something that was claimed un-doable; the obvious case is George Dantzig. But that case also shows that any scientist or mathematician who can be shown an error in something thought impossible will be thrilled at the discovery, because that is new knowledge, which is the whole point. Poking a hole in the rules of the contest, finding a weasel way around them, is not something interesting at all.