The predominant big-game animals when pioneers entered the Salt Lake Valley were elk and bighorn sheep. There weren't many deer.
One reason was hillsides were covered with grasses, which was a good food for elk and sheep but not for deer.
Unrestricted hunting nearly wiped out what deer Utah held. Lawmakers responded by closing hunting from 1908 to 1913, then after 1913 only bucks were fair game.
Overgrazing turned what were lush fields of grasses into barren wastelands, which allowed browse and forbs, main foods for deer, to grow.
The deer responded. Numbers increased rapidly. In contrast, elk and sheep numbers fell just as quickly.
To control the rapidly expanding deer herds, Utah started in 1951 allowing hunting of both does and bucks. Hunters, in fact, were allowed multiple permits to hunt multiple seasons. Deer were numerous and big bucks common.
To slow the falling deer numbers, Utah went back to buck-only hunting in 1975.