You only want the string to vibrate between the nut and saddle. Anything beyond this results in loss of sustain, confused harmonics, more difficult intonation, and so forth..
Sharing a bridge does run the risk of transferring vibrations from one string to another, but that's a somewhat different problem (pause for a moment, as we contemplate the design of a piano...).
I'm also intrigued by the massive individual tailpieces on the Spyder (which I suspect arose more from visual than vibrational design), but I still think it's more important to clearly define an 'end' to the string, at the saddle.
As it happens, I'm experimenting with a small brace beneath my bridge, such that the height adjusting screws will actually be pulling the bridge down against the brace, and the bridge will be prevented from rocking along the length of the strings (and generally vibrating less).
My first attempt last week was negative - for whatever reason, I preferred the sound without the brace. But it was also too high, so I was hearing some other effects (e.g. as if I had lowered my pickups). I shaved it down this afternoon and may get around to trying again later tonight.
As you say, questions, questions!