"A very heavy bag may help your fitness and power, but it will not help your movement much."

Not necessarily, it can still help your movement, not just fitness and power. The thing with a heavier heavy bag, is that it will swing when you need it to, via a push and not a punch.

I don't advocate hitting a bag that is practically immovable, but for realism sake it's a good idea to have a bag that can respond in some ways like a real opponent.

Floyd Patterson, in his "how to box" book warned that using heavier punching bags may lead to a lack of footwork. Although this may hold true, it can be prevented by keeping your opponent in mind while working the bag.

I suppose that in a perfect gym you can an "a la carte" choice for bags allowing you to work on many different things.