A smoke stack that high has to be very strong to keep from collapsing from its own weight. In the 3rd photo you can see the walls are at least 2' thick, and they are likely thicker as they go down.
You would need a good swing to put a dent it that with a wrecking ball. So much so that I would think it would be impractical, (i.e. the boom would have to be almost twice as high, and I'm not sure you want to shake a boom that long as violently as a wrecking ball would.)
They could have used explosives, since they did not, this opens the possibility that there are nearby structures that they did not want damaged.
The fact that they went through the trouble to put an excavator with a hammer up there, suggests it was necessary.
Just the ride up there is probably more than most people could take.