Such ID transmitting devices already exist. They are, however, obscenely expensive (at least 2-3 times the cost of most craft) and fairly battery hungry. They also require an ID number which would mean having to go through the costly process of getting formal aircraft registration. Their weight and power draw would also affect the performance and flying time of, particularly lighter, craft.
Part of the problem faced by drone owners is the success of DJI. They have become such a market leader that their products, particularly the Phantom, are what the public thinks of when drones come to mind and their capabilities are assumed by the public to apply to all UAVs.
The heart of any drone is the Flight Controller (FC.) It manages the craft and converts the control inputs from the sticks into control signals that direct the motors. Unlike a model plane, where the stick movements can be directly translated into movements of the control surfaces, a drone can't fly without an FC.
Not all FCs support geofencing around airports. In fact, most non-DJI units don't. Not all FCs have GPS as standard or at all. It's not desirable on grounds of weight or battery life in some applications such as drone racing which is performed with small, very fast craft where agility is much more important than stability. Not to mention a lot of drone racing being done indoors.
Would any legal restrictions require onerous technical inspections to check the capabilities of craft? How do they know that my GPS-equipped FC isn't running old firmware from the pre-restricted days or I haven't unplugged the GPS cable? Would I need to have it re-inspected every time I did significant work on it?
As a user and author of open source software, I have concerns about where this might lead. If GPS and geofencing that couldn't be defeated were to be made legal requirements, that would effectively constitute a ban on all of the open source FCs as they either wouldn't have geofencing or any miscreant could edit the code or the no-fly-zone list to remove the restrictions. I'd hate to see a precedent set and it become normal for open source to be banned from whole classes of products because of what someone might modify them to do.