So yes, I think it's a fair question - crosswind (and head/tailwind) data could be calculated continuously and automatically, and given on RT in the same time, reducing the mental workload of a pilot who may well already be working fairly hard. Automation would eliminate additional ATC workload, and there's nothing to stop the more conventional wind information still being available on ATIS or on request.
Genghis
Cross wind component is rarely static. Lets look at the situation where ATC are calling out winds for your information as I posted above 220/15 240/30 270/35 200/10.
You have given yourself a crosswind limit of say 15 kts ?
Now I can land ? Now I cant? Now I cant ? now I can?
Its the big picture, your ability and the aircraft limits not the demonstrated limits. What is the windshear like? How constant is the wind and its direction ?
These are all questions which determine whether you chuck away the approach and go elsewhere.
Pace