How would you not catch a deer?
By selecting trails used primarily by hogs, adjusting loop diameter and height, and using deer stops to make it easier for deer to pull a foot. Also you can use jump sticks to encourage deer to go over and hogs to go under.
Nothing is 100% foolproof. A deer or hunting dog can get hung up in a water set snare or body grip trap. Rare but it could happen.
A lot of deer are injured in closed top guillotine door hog traps each year. Usually with broken jaws from hitting the wire/panels. It's just not mentioned very much.
I still say that they can be a cost effective tool that could be utilized under tightly controlled situations.