What other loads might there be that have a 'spiky' current waveform and high current, that persists for several hours?
I don't know - quite probably none. As I recently wrote, EC chargers are probably fairly easily identified, but the same is not true of most of the other types of load that some people fear Big Brothe will be monitoring and maybe even 'controlling'.
Another thing that seems to get overlooked is the fact that (at least with current installation infrastructure) the currents being drawn by all loads arrive at the meter through the same cables, as a single 'composite' current, which presumably would/will complicate matters. What if, for example, an installation is powering both an EV charger and storage heaters during the night. The system may well be able to find strong evidence that an EV charger is part of the mix, but working out how much of the total current is attributable to that load, and 'meter' it separately, could well be a challenge.
A 'smart' EV charger could, I suspect, not only 'identify itself' but also 'report' how much power it was consuming. However, creating a reliable IT system that could constantly monitor 25 million (or whatever) electrical installations would presumably be a far from trivial task.
When one considers how long it takes us to build a railway line or extra runway capacity at airports or device an NHS-wide IT system that actually works, I do wonder whether there is much prospect of much of these feared happenings getting very far this century! It's certainly not something that I personally am going to loose any sleep over!
Kind Regards, John