I have a Yamaha TW200 setup for hunting and love it. I chose this bike for several reasons. Yamaha has not changed it since 1987 so parts are easy to find, lots of third party after market add-ons and accessories are available (larger capacity gas tanks, windshields, hand guards, etc), easy to work on, low seat height, and light weight. They come from the factory to be street licensed, but are designed for on and off road use.
There is a TW200 forum and here is the link.
https://www.tw200forum.com/index.php
One of my hobbies is to fabricate things. I designed and built a tail rack for my TW200 so I could carry a rifle and other hunting equipment. I could not find an aftermarket tail rack designed to carry a rifle. Here is a picture of the tail rack I built which is made out of 3/4" EMT conduit.
The end of the rifle case is tied to the passenger foot peg and the rifle is removed by unzipping the top of the case and pulling the rifle out.
It is not practical to haul a deer or an elk out on a motorcycle. I just gut and tag the animal then return to camp and get my truck.
The disadvantages of hunting off a motorcycle are cold weather, muddy or slippery conditions, and limited cargo space. There is a safety issue with falling over too.
Advantages are gas economy, mobility, faster to get around, smoother riding than a quad, and it can be transported without a trailer.
To haul my motorcycle around, I fabricated a hitch carrier that I can swap between my pickup and travel trailer. It is also nice to have a street licensed motorcycle for alternate transportation if needed.