I used to work as an explosives chemist- including once at one of the favorite facilities for Mythbusters- so maybe I can make a constructive comment or two.
Ammonium nitrate (AN) is used for stumping fields for a lot of reasons. First off, it's cheap. ANFO is just about as cheap as you can get in terms of "bang for your buck." When you're dropping iron bombs, cost isn't so much of a concern- even moreso with torpedos- so more expensive stuff is used for these applications.
Secondly, it's highly insensitive; ANFO either needs to be sensitized with other compounds (aluminum flake, for example), or a large booster has to be used in the firing train for it to be reliably detonated. Even then, most of the large shots I've been involved with used two independent firing trains, making a fizzle much less likely.
Thirdly, ANFO for stumping fields uses readily available components- a sack of AN (which, I note, can still be purchased locally- for now- with no special paperwork), and any one of a number of hydrocarbons like diesel.
However, ANFO has a particular property that makes it amenable to stumping, which is that it provides less brisance- more "heave," and less "shatter." If you're moving rock, it's undesirable to move just a few hundred pounds that have been reduced to powder; normally you want to move a few thousand pounds that have been reduced to cobbles. It's the difference between being punched in the shoulder, and being shoved; given the same amount of energy, the effects will be dramatically different.
AN *can* be combined with other fuels to provide much greater brisance- anhydrous hydrazine comes to mind, but that's dangerous stuff even by the high standards held for explosives. Moreover, it's toxic and hard to store.
As an aside, it is disappointing to see Mythbusters using the "big shot in an open field" technique. They have a bigger budget, and should have gone somewhere that specializes in that sort of thing, like they have in the past. This obviously wasn't the right venue for a quarter ton ANFO shot. Noise abatement is a big part of dealing with energetic materials, and whomever they had on the job to make that assessment screwed up pretty badly.