Okay, lets say there's a slick, smooth-as-snot implementation. The software is perfect, it works in any browser - even mobile- without plugins. User navigation is natural and intuitive, and it has a high frame rate even on obsolete devices.
Well you still haven't described 99% of the web. What do people use the web for?
1) Interacting with people. 3D chat stinks and always will. Even fully realized 3D worlds like MMORPGs chat has nothing to do with 3D, it's essentially IRC. 3D email's a looser. Email is best navigated as a list.
2) Finding information. But most information is best displayed as a 1 or 2 dimensional list. You can read pages of information, not 'volumes'. You're already looking at a virtual screen, watching videos or reading on a virtual screen within your virtual screen is a needless and distracting abstraction. And navigating a 1D or 2D space is much faster than 3D. Seriously, try finding the entry you're after in a 3D room full of Wikipedia. You don't want to have to look behind the article on Aardvarks to find the one on Abe Lincoln.
3) Porn. And having been around the net a bit I know there's some CGI porn out there, it's creepy as hell, and that isn't changing until people want to fuck at the bottom of the uncanny valley.
4) Shop. While I'd love to have full 3D fly-through of every product I shop for, it's not going to happen for several reasons. First, preparing 3D models of products that look as good as a manufacturer wants it to is incredibly time consuming and often futile. They'd much rather customers see a heavily photoshopped glossy product image. Second manufactuerres don't want people to have full 3D models of their products. It sets the intellectual property lawyers on edge.
Those 4 cases cover 95% of web use. So no, it won't ever 'take off'. It will always be a niche.
(Source: My experience working, for various clients on an alarming number projects that tried to do the things above in 3D, dating back to 1996. All of them were embarrassing failures.)