I've just finished my PhD, so I'm an expert in a very small field.
Yes, it is true that I've read a good paper that I do not care whether it is peer-reviewed, on arxiv, or just on a homepage. As long as it is of good quality and there is a way to cite it, I'll probably cite it in one of my own articles.
However, and I'm not saying this out of defense for the current system, you must understand that the system is also in place to filter out some of the complete and total crap some people dare to call research. I've reviewed articles that made my toes curl, because of bad grammer, bad presentation, or just duplicating another article with 10% of the article changed.
Already at the moment there are so many journals and magazines that I have to keep track of that I simply don't have the time to search the web or dig up things on arxiv.
I simply have to trust some system to filter out the good articles.