it doesn't hold water in the case of a gyroscope.
I was speaking to professionally designed products as opposed to just a demonstration of the gyroscope principle. You sound like you have some EE experience but I wonder if you are seriously suggesting that someone would attempt an all-analog control system for such a thing. Even little remote controlled toy helicopters now use DSP for that purpose, and their part count is extremely low.
Sure you _can_ do a gyroscope with a few op amps, but if you're actually going to make a segway-style product then you also need steering, low battery safety, tip-over safety (ie jog it back upright if you're going too fast), and so on. It also needs to be reliable and manufacturable, and with a micorcontroller-based design that is a lot easier to do because you can have self tests (factory and power-on) that sanity-check your inputs and such. And you can do all of that very easily in a $2 micro.
I'm curious what actual products you can think of where such low-speed analog control systems are preferable to a nearly-free microcontroller. I have the habit of reverse engineering nearly every new electronic device I buy and have not seen that kind of implementation for a loooooong time.