I created a screen font, as an experiment. It is not that interesting, but it seems relatively consistent, and it fits the pixel grid well, perhaps too small for common use. It seem screen fonts are not that popular, X windows uses scalable fonts, and mozilla went to softened scaled fonts. Matthew Carter created fonts oriented to the screen by first creating optimal bitmaps and then fitting outlines to the bitmaps. For the usability people here, it might interesting to measure the readibility of different fonts on the screen.
In a web specification, I would probably only specify bitmap fonts. They are very easy to display, and don't give preference to any particular font description. How fonts are designed might evolve independently. A good compression method would be needed if bitmaps are used, this might be a canidate but I don't know of data is sparse enough. Different bitmaps could be sent depending on the device, high resolution bitmaps for a laser printer, optimized low resolution bitmaps for a typical display. The properties of the device could be sent in the request. This pushes some of the complexity of the client into the server, the server would likely cache all common requests, and likewise the client cache fonts only downloading upon need. To anticipate a likely objection, bitmaps could specify 256 levels of gray to achieve softer characters for screen display.
Characters as shapes might be best addressed seperately, rather than generalizing this with text display.