I think that part of the problem may be the numbers of deer in the Highlands being unnaturally high for the estates’ shooting interests.
If this really were the case, then the Deer commission, then SNH, have had the power to impose cull levels on estates for decades.
The complex answer is ‘it’s not as simple as that’, there’s myriad factors at play, including Increases in deer population to exploit food availability caused by the reduction in woolly maggot numbers, plus increases in woodland Roe population to exploit food availability caused by the increased red deer culls
https://www.bds.org.uk/index.php/documents/146-deer-mgt-report-6417/file
Personally I think that fences are a big part of the problem, they interrupt the natural patterns of deer migration into the woods in winter, leading to overgrazing on the moor and those areas of woodland that deer can access – I have felt for some years that ‘lots of little fences’ protecting smaller coupes of regeneration within forests would produce better results than huge perimeter fences to keep the deer out entirely.