Even if a website is not required for your application (and I doubt it ever is), it is an additional helpful resource that allows you to elaborate in more space. The larger adcom committee most likely won't look at your website.
But, once you are past the initial phases of the adcom, the individual professors choose who they want to take on in their labs. A student who has a website will have more information to offer. A professor can look at the website in his/her own time, versus a larger adcom. (The professor I recently spoke with already looked at my site, and it's pre-application.)
You can call it "unfair", because you added more resources than the standard application asked for. Or you can call it resourceful and driven to take the time and effort to make a good website. A website shows that you aren't afraid to put your research in the public view, and shows that you are serious about displaying all you have to offer. Additionally, a website allows the professor to click hyperlinks to your publications, organizations, programs, etc., which is a feature unavailable on a printed application.
In the end, you don't need a website. But it's not unfair to create one and show the adcom. You can get in without a website, because your work should speak for itself. But a website can also be a way to explain things in more detail and advertise your work (within and outside of the admissions process).
Also, I view the website as something to show professors when you contact them about admissions, not something that you expect to be an option in the application. Leaving a link to your webpage in your email signature is a great way to get noticed by different faculty.
I think we should all just agree that:
- A website is not necessary, but it can be helpful
- You should spend time on the parts of your application that are required, before optional parts
- A website is most helpful in the latter parts of the application process or while contacting professors early on