Tree dogs that break themselves off of deer by running deer. Based on my experience, which isn't as much as some here, and largely my opinion, there is a reason for that, if you study them closely. Look at their build, and their feet and legs. Then compare that to the look of a good bred running hound. Most of the "naturally broke" dogs I have seen were bowed in the front end like a bulldog, had big flat paddle feet, were extremely large, and sometimes kept too fat. Any one or a combination of these. They quit deer because they can't ever get close enough to them to keep up with them and it hurts too much. They are getting shocked by their poorly put together bodies every time they take a step after the first mile.
Never seen a good built tight footed fast dog that was naturally deer broke, unless it had some cur in it, and those just because they seemed to be more attached to their handler and didn't like to get too far away from their handler, unless it was something they could look at every once in a while, either up a bush or fighting on the ground every once in a while. Most of the curs I have owned or been around were just different, they wanted to tree, catch or fight with something, and if they didn't have any reasonable expectation to do those things they stayed in spitting distance.
Wonder if anyone has ever thought of crossing cur with running dog, like recently? In my opinion , based on a lot of reading and some of that between the lines, that is how a lot of coonhounds came to be. Keep in mind, coon hunting is a recent thing. Every body fox hunted until roads were good enough to run over dogs, and then rural people got mixed together in WW2 and picked up bad habits from those southern boys and started stocking coons and leaving perfectly good fox dens standing instead of cutting them down on the ground where fox could use them.