It''s an interesting idea, at least!
I think that you could actually use it and make it turn out well. Have the arenas actually set outside though, like the mouth to a cave, and the dragon''s in the cave. The master of the animal need not be there, since they could bond to the animal remotely.. that way you never get killed while the guy collects up the dragons that you fail to protect..
I like the idea of making speed be a factor, but you need to add in endurance. The slowest creatures can usually go for longer, believe it or not. Look at the heavyweights in boxing, if they fought a lightweight, they would most likely be outrun, but they could last for a long time simply because the lightweight couldn''t hurt them as much. It''s all dependant on things, i think that''s why most games force you to balance between endurance, health, strength, and so on. It''d be interesting to see what you could make with this though