I've thought about this before because it would be a lot simpler like you've said. I find there are a number of issues that would make an analog gimbal much less effective than an electronic based gimbal. Like RcPro97 says, it will probably wobble around a lot. The only force working to keep the camera in position is gravity, which is constant. So any movement from the aircraft, fast or slow, is going to result in the same reaction from gravity, which is constant. Electric gimbals have PID loops that account for variations in the movement of the aircraft relative to the gimbal. With a lot of weight an analog gimbal might hold pretty well, but then you are adding a lot of weight to the airframe. Another issue is that you can not deal with yaw with an analog gimbal. Maybe with enough weight you can increase the moment of inertia of the gimbal enough that it does not easily rotate when the aircraft yaws, but then again you are adding a lot of weight.
Overall an analog gimbal will not work as well as an electronic one. But it is a concept that I think should at least be attempted to see what happens. If you are not aiming for very clean AP work then maybe an analog gimbal could work.