The worst thing that could happen to Project Euler is that it goes offline and doesn't make the questions available. The second worst thing is that it stays online, but doesn't let you know if you've solved the questions.
I was going to add the third worst thing would be for Project Euler to stay online, validate answers, but not add any questions - but, really - there are enough questions now to keep me going for a couple years.
Perhaps you and I look at PE differently, but, I do not care at all how many other people solve, or don't solve questions - beyond giving me some insight into how difficult some questions are, and whether I am missing something obvious.
Solving PE problems is a reward in and of itself - I would never be so douchey as to point to my PE Profile - For one, there is no way of determining how long I took to answer the questions, and, even a scripter of my incredible limited means, can answer most of the questions with enough time and effort.
I think PE is one of the great gifts on the Internet, and, while I think anyone who actually uses a "show answer" tool is being retarded, and both (A) completely missing the point of PE, and (B) robbing themselves of the experience of solving the problems - the only person who is being hurt by that tool, is the person using it, not me.
So - I perhaps agree with you that the feature is a Bad Idea(tm), that does not bring value to it's users, but, at the very least, does not impact me negatively.
* What would have been cool by the author, is that instead of giving answers, would have been to give hints pointing to various algorithm, or mathematical concepts. For example, there might be a question that is trivial to answer if you know (and can implement) Dijkstra's algorithm - and 90%+ of the value of the question can be reaped by reading up about Dijkstra's algorithm, seeing how it applies here, implementing it.
I'd still like to spend an hour or so on my own, but if I run into a wall, simply getting a hint that says, "Dijkstra's algorithm" or "Trémaux's algorithm" would still let me capture most of the value of the question.