It is certainly not a bad idea to use tomato cages for your tomato plants. After all, they provide lots of great support for all that heavy fruit! And I know you just read a great book called "Cubed Foot Gardening" about intensive gardening in raised beds, and that the author emphatically recommends using cages or stakes for tomatoes. And yes, I know that the bamboo stakes you bought are really too small for such vigorous plants..you really probably should have bought thicker stakes.
So while cages are indeed great, the trick here is...(are you listening carefully, Self?) to put them on when the plant is still very small. Trying to wedge one onto an already ginormous, multi-branched plant is really, really not a good idea, as you have just learned. It does, in fact, result in major wreckage, accidentally breaking off one whole branch (which had almost ripe tomatoes on it, I note...way to go, Self!), damaging many other branches, and deeply abrading the main stem. If you'll recall, you ended up half in tears, grass stains on your knees and alternately cursing and apologizing to the poor plant.
Please remember this for next time. Your consideration appreciated.