This is a myth. Never seen or heard of a pack of dogs catching a healthy deer, in fact I have seenalotof deer that have been shot still out run the dogs.
You have never seen it because you live in Florida where there is no snow.A pack of dogs can run down and kill a deer with deep crusted snow.
Personally,as far as I am concerned,if it is legal where you hunt,and you keep the dogs on your own property,I have no issues with running deer with dogs.Not that I would enjoy meat that is full of adrenaline from an animal being chased.
However,it is illegal where I hunt,and any dog seen running deer is usually shot on sight.