I had similar thoughts recently, although without quite the glorious bicycle collection to go with it.
I'm not of the opinion that electronic shifting is a game-changer, at least not in its current form. My guess is that hydraulic braking, at least for road bikes, is not either. Disc brakes might be, but like the above, there still lie the constraints of weight, given as how gravity is and will always continue to be a bitch.
The basic design of the bicycle hasn't changed in 100 years. I think that's why people like us love them so much - there is such an obvious elegance to a design that is so nearly perfect out of the box. And I guess the idea that it might all go out the window in a relative heartbeat is a little scary, not to mention expensive.
But in terms of game-changers, I think that there are some potential ones, and I'm sure they're sitting on somebody's prototype table today. I think VN mentioned the idea of not only electronic shifting, but intelligent electronic shifting, so that each shift reflects not just a change in cog, but a linear change in gear ratio. This would actually be a value add, IMO. Another, and this is a natural step, is wireless shifting (and maybe braking). If you take wires completely out of the equation, then the benefits to calibration and aesthetics suddenly become interesting. And the last one is some form of continuous variable transmission - CVT. If I recall, people have been playing with that one, although I suspect it's greatly aided by electric guidance.
Of course, all of this is dependent on weight and aero concerns. The idea that electronifying the entire bike will have insurmountable obstacles is probably a temporary one, but one that will certainly take some time to figure out. But to me, it seems to make more sense to wait until the entire bike is electric (at least except for propulsion), than to pick these technologies up piecemeal, which is obviously a cumbersome and painfully expensive way to do it.