Not a goofy idea at all.
Contrary to much of the so called expert opinion in the cycling trade, tall top heavy objects actually fall over more slowly than shorter ones. This is not just opinion as it’s down to the laws of physics. There is even a branch of physics called “inverted pendulum theory” that explains why this is so.
http://en.wikipedia.org/wiki/Inverted_pendulum
The physics works for all top heavy object balanced objects, including bicycles. Apparently, The taller an object the slower it falls and so the easier it is to keep balanced.
You can experience this when riding a Penny Farthing. Which though very tall and top heavy is also remarkably easy to balance. Especially so when moving forwards at very low speeds.