I clearly remember, back when I cared about Utah deer management, reading a F&G official's report from 1968 in which he suggested 800,000. The gist of his report was that 800,000 couldn't be sustained and that a population crash was imminent. The number was probably bogus, but it really doesn't matter. What matters is the fact that in the years that followed, the state's deer population did indeed take a nose dive (for a bunch of reasons).
At that point, hunter preference began to replace biological science in deer management. In response to growing public pressure, the state abandoned the use of hunting as a management tool in favor of management for hunting. Since then, there's been a sustained effort to reduce harvest, mostly by restrictions on hunting. In 1975, general season permits went from either sex to buck only. The late 80's saw limited entry, high country and 3 point or better hunts. In 1993, hunters were required to hunt only one season and in '94, permits were capped. In that same year, any weapon permits became regional. By '99, all permits had to be purchased directly from the DWR.
For all practical purposes, we now have statewide limited entry. And still, after decades of restrictions, hunters complain about overcrowding and too few mature bucks.