Another aspect to this debate: it probably makes sense to differentiate:
1. injury prevention
2. foot and leg fatigue effects
3. technical features
Across 1 and 3, I think there can be debate, for 2 it's a no brainer that a super lightweight boot would do better than a heavy one. Weight may get you benefits for 1 and 3 but it can only be a negative for 2.
For 1, I am pretty sure a minimalist boot, when similar footwear is worn for all other periods of activity, too, does best most of the time: strengthening ligaments and joints is better than wearing a cast that may or may not absorb bumps. Even in bad terrain, the leverage exerted by a stiff shank may lead to injuries in knees (which are typically worse than ankle injuries) when a slip or fall is experienced, even if it saves your ankle. Moreover, I'd argue with more feel to terrain and greater toe splay flexibility, you will prevent a number of falls or tumbles before they even happen. But I will concede that it's not a "100% of the time" thing --there can be terrain and setups where injury risk is reduced by a heavy boot. I'd just want people to be realistic about how often they are in that terrain. (This also exempts say safety capped boots in machinery or forestry work or fire fighting boots -- no question injury prevention is the imperative there, but that advantage just doesnt apply to hunting !)
For 3, the heavy stiff boots will have an advantage when there are technical features or moves that they enable -- snow shoes need something to clip to, digging into skree or snow, ... you wouldnt wear a flexible boot inside a ski binding either

But again, how often do you actually hunt in a mountaineering skree field?