Just thinking about it mathematically, if you hit a big enough rock with any wheel, it will probably nose you over.  Having three wheels instead of two lowers your chance of a prop strike by 33%.  Then again there is the weight issue.  A big heavy strut with a big heavy tire forward of the CoG, especially when most bush planes are light to begin with, isn't ideal.
The only common light bush plane I found with trike gear was the 801.  A few had big balloon tires all around.