To shoot deer with a rifle you have to first prove you should have a rifle legally for that purpose, then be tested before you shoot. Therefor the propect of a wounded deer running off with a gut shot is remote. As anyone can get a bow , that level of scrutiny isnt available . Even if bow hunting was only allowed by permit , any idiot could still buy a bow and do it illegally , not so a rifle.
My knowledge of this comes from having worked in a wild animal rescue hospital, I have seen many wounded animals brought in with cross bow bolt injuries.