Already possible with CRTs
LCD shutter glasses and the like work very well with regular CRT monitors. You can either drive the glasses with a pass-through adaptor that sits between the device generating the video signal and the display (used for watching stereoscopic VHS/DVD for example) or have the device generating the video signal drive the glasses too (Segascope 3D on the old Sega Master System did this). You don't need a special TV set.
The reason this works is because a CRT will display image data as soon as it receives it. When the device generating the video signal sends a scanline to the display, that scanline is shown on the display. An LCD (or other modern flat panel display) may store a frame of data in memory and not actually display it until the whole thing has been received (incurring a delay of at least one frame). This delay becomes worse in sets that perform additional processing of the input signal, and is the reason that rhythm games have a configuration screen that lets you compensate for the lag between the picture and the sound. As the picture on the screen is no longer in sync with the signal being fed into it you can no longer accurately alternate between the sending images to the left or right eye.
If you hunt around online you'll find a variety of circuits that can be knocked together at home to drive LCD shutter glasses. I use such a circuit with an old 17" CRT and some £11 LCD shutter glasses I acquired on eBay to great effect.