That's exactly what is happening these days with custom font embedding having become practical (in web pages): http://somerandomdude.com/2010/05/04/font-embedding-icons/ (that was in 2010, but this thing is really gaining traction these days following the release of "Font Awesome" for Twitter's Bootstrap)
In desktop OS, that is in fact a very old technique, that's why the Marlett font exists in Windows .
It does have a significant inconvenient though: the icon can only have one color for the glyph and one for the background. This provides a crisp look but lowers the expressivity of the icons. On the other hand, if the color scheme changes for some reason (or can vary from one page to an other), it is very easy to match the icons's color scheme to that of the application.
I suspect that there would be a whole host of other issues (rending of baseline location varying by a pixel, etc.).