Technically, it could be possible to construct a hunting regime that would mimic wolf predation but in practice it would be extremely difficult. The power of natural predation is the coupling of predator and prey population sizes, who the wolves target, and how hunting success varies across a landscape. The wildlife management body would need very high resolution deer population data (unreasonably high), strong predictive models, a hunter population willing to accept sometimes dramatic yearly changes in tag offerings, and the hunters would need to mimic wolf prey selection (young/sick/injured/old). That is without taking into account the complex behavioral interactions around the landscape of fear wolves create or the non-deer predation that wolves perform.
One could hypothetically kill ALL of the deer but then you just create a different suite of problem. Herbivory resistant plants get outcompeted, nutrient cycling drops dramatically, and you have to invest a lot of money to keep new deer from colonizing the area. Plus, from a parks and tourism perspective, if you just kill off animals larger than foxes then you’re left with less appeal.
(for context not authority – I’m working on a phd in food web theory)