Removing all the politics and hidden agendas (real or imagined), I think there are several things that need to be considered:
1. There is fairly good reason to believe that, over much of Scotland, the deer population is higher than would be optimal. This is both from the perspective of maximising the quality of the animals shot by us, and from the perspective of anyone attempting to re-grow forest.
2. For many estates (possibly the majority), the economics of hind culling do not add up, so they tend not to shoot as many as would probably be optimal. So the population tends to grow.
3. In the very long term, it would actually be in our interests (as stalkers) for the populations to be radically reduced for a period, allowing forest re-growth. Then allowing the population to grow again, but in woodland rather than open moor. The available evidence tends to suggest that this would increase the quality of the beasts (meat weight and antler size).
Now re-introducing some the politics...
SNH et al are conviced that the deer population needs to be reduced. They are probably right (though maybe for the wrong reasons). The very simple fact id it that, if we (stalkers, estates etc) are not seen to be making concerted and effective efforts to reduce the deer population, the government will become more proactive with regard to legislation and dictating culling plans, possibly moving toward doing it themselves or taking deer into public ownership.
So it is in our very best interests to forestall moves by the government by finding ways to alter the prevailing attitude toward management on private estates, and to be seen to be reducing the deer population. Quite simply, if we don't do it, they will - and we will lose out, very badly.