And let's not forget that in many places, a tripod is not allowed (a football game is a perfect example) because it would be dangerous and impossible to move quickly.
But museums are also another example. Often, if they have a "no tripods" rule, you can draw that line in the sand and use a monopod. ("The sign says 'no tripods' officer, not 'no monopods.')
It's hard to conceive if you've never used one, but it does give you more stability- you'd think it wouldn't because it can still move around, but somehow, it does. It takes away a lot of random shaking.