The USA approach to this is to mandate a comical number of outlets everywhere (to prevent extension cord usage), mandate a large number of individual circuits (especially for things that draw a large amount of power), and more recently some combo of AFCI/GFCI/CAFCI breakers (to provide some level of sensing things going wrong and shutting off power).

The stats are not great for the USA in terms of number of fires. I haven't done deep research. From personal experience, most homes built after modern US electrical code was fleshed out are generally fine. Modern homes (or ones upgraded to modern code) seem very safe - the "smart" breakers tend to actually work.

My anecdote here is that my relatively small hometown area (15,000 people, largely built up between 1860-1940) still has frequent fires relating to electrical and heating systems and the current city I live in (95,000 people mostly built up starting in ~1960) has very few fires ever. I spend 2 weeks a year around Christmas back in my hometown. 3 of the last 7 years had a structure loss fire while I was there. In the same period of time there have been 2 structure loss fires in my current city total.

And Europe doesn’t have old houses with the same difficulty in wiring?

So you’re not saying it’s because the wiring is substandard, but because it’s ring circuits, which are not up to the same standard as if they used a breaker panel.

Isn’t that the same thing?

You know that extension cords can have breakers or fuses in them?