There is a proposal kicking about for notification above 12500lb (5700kg). This is being resisted because it catches a lot of stuff like King Airs.
Presumably it would apply to USA only. It would be totally mad to do it worldwide.
There are big concerns (see the US AOPA newsletters, etc) that if the 12500+ regime did come in, it could get extended to all the stuff below too. That would be a real problem.
It's all a bit meaningless since I am sure that anything 12500+ will be filing a flight plan anyway, and all the agencies see those real-time anyway (as they do in the UK). I suppose such a notification would be just another website to hit, but collecting the required passenger details for a domestic flight would be pretty intrusive.
The GAR form is a big enough hassle sometimes, collecting passport numbers etc.