Would it be worth thinking about the question, what’s a specific thing someone wants to do with OSM data that they can’t do right now?
If you want to find “areas of land covered with trees” you could treat all areas tagged natural=wood, landuse=forest and landcover=trees interchangeably. You could also exclude areas below a minimum size to catch small groups of trees that have been “painted” using these tags.
If you want to find all the land commercially managed for timber production and landuse=forest doesn’t work because of how often it has been used to just mean covered with trees, then may I suggest produce=timber? Though many commercial tree plantations do not have the tag, at least you’ll know that those areas that have been tagged with it are used for producing timber. More areas deserve the tag, so we should probably go and map some more.
Do we have a tag that is similarly precise (if underused) and means old-growth forest?
The advantage of introducing and promoting new, more precise tags would be that it doesn’t require any tag deprecations.