The trouble with that is all our game animals were provided and acclimatized with the goal/Intention that hunting should not be only the domain of the wealthy anybody should be able to hunt, and also as a protection for some species that were in a threatened population in their home ranges.
Returning the land to pre European settlement as @
Pengy suggested is flawed as the first settlers the Moriori and second settlers the Moari had already hugely modified the land with fires and hunted/destroyed habitat of many species into extinction and pushed many others to the very brink....this was all well before the arrival of the evil white man and introduction of deer/pigs/thar/cham/goats/sheep/stoats/ferrit/possum/rabbit/hare and all those other things that provided a means to stop eating each other to survive.