So a flywheel will keep you from falling. It will do this, however, by keeping you from moving. The physics are complicated (especially for me, considering Dynamics was like 18 years ago) but... Here, look. Ever seen a powerball?

Flywheels work through rotational inertia. Force applied against the axis of a flywheel is translated through rotational inertia in another direction. This makes them stable, and that stability is why flywheels work for positioning. BUT the more stable that flywheel, the more rotational inertia they have... which effectively means the more resistance to moving they have, not just resistance to "tipping."

Flywheels work great to keep you in the position you want to be in. If you want to be in another position, though, flywheels work against you. So while a flywheel will keep your walking automaton upright, it will also increase the amount of force necessary to, say, go up stairs. Or move to one side quickly. Or translate in a desired direction. They aren't without their drawbacks. This is one reason why racing motorcycles have carbon fiber wheels - the flywheel effect from aluminum makes them handle with less agility.

On the other hand, if your MEMS sensors can sense the way a flywheel gyro can without imparting the moment of rotational inertia you get from a flywheel gyro, you can get the benefits of a gyro without any of the drawbacks. That's why everyone went solid-state long ago.