So people are happy plugging in cabling into a circuit with no protection?

It’s less about being happy about it, and more about ignorance, industry/legal inertia, and the complete lack of me being the global benevolent dictator for life. Sure some might initially resist my efforts, but they’d come around after receiving an appropriate reeducation at my fire safety camps.

There is protection, just not at the cable itself.

UK only needed to introduce that because of their ring main architecture, which was fused at levels above a plug.

Also c.f. extension coils and pre-battery vacuums: both needed their cable full unspooled to reach their full load rating. Yet they typically lack technical enforcement mechanism to not rely on users being literate and willing enough to RTFM.

What provides protection for a 3A cable plugged into a 15A outless?

Safety margins in what you call a 3A cable. And each circuit being fused at a lower 16A, not the 30A that my British house had.

Something like 1.5 mm2 (only a 0.5mm diameter) is able to handle 12A if the insulation survives heating up to 60 degrees and 18A if 70 degrees is acceptable. The whole circuit would have a 16A fuse at the fusebox, so you're not going to get to 70 degrees.

Far from ideal, but also very very unlikely. Because a short would be over 16A and blow the fuse. So we're talking about some situation that's far from a normal load (any device that's close to such a load would need a different cable to be certified), while still remaining right under the maximum load of the fuse that's covering the circuit.

Homes aren't burning down all over the rest of Europe all the time, while fuses in plugs aren't a thing here.