Our breakers
I would say almost all US homes have breakers. Even those with legacy fuse boxes have breakers between them and the service. There are six major types of service panel, and all 6 designs were settled in the 1960s. I have a 1960 CH panel that takes modern CH breakers. This video represents our standard layout (except the 240V breakers on that "QO" type have only a single handle, oddly.)*
Some older houses still have fuse boxes for lighting. This is because in the past, they did only a partial re-wire, and left the original fuse box in-place to feed typically lighting circuits. It is wired as a "subpanel" fed from a breaker in the new circuit breaker panel. We have that in this 1924 home.
The USA is a 240V country actually; we just use a center-tap to get half voltage for small circuits. The above video explains it all. **
It would seem to me like in most cases it would be difficult to reliably/systematically get the Earth loop resistance low enough to allow the fuses to pop when there is a short to an earthed enclosure.
Actually no. Earthing has been required starting in the 1950s and on all circuits (except dryers and ranges) since 1966. Further, USA earth wires are always the same size as the live conductors up to 30A; we don't shrink earth like Europe does, until you get to 40A or larger. Even then, Code calls out a minimum size for earth to assure it can clear faults (trip breaker).
Also up to 30A, we limit wires to their ampacity at 60°C thermal. For instance our 14 AWG (2.1mm2) is only allowed 15A breaker (and most appliances also have an 80% derate, so for instance a 30A dryer or water heater does not exceed 24A draw, and most plug-in appliances with 15A plugs don't exceed 12A.)
My guess is that with 120VAC instead of 230VAC, most of the issues become fire hazards due to overloads, and much less electric shock - but I suspect that 120VAC can still be dangerous and lethal in certain situations which are not that rare. Is this why local GFCIs (as in, for a single socket) exist or why I find the sockets here ludicrously dangerous compared to most European plugs?
120V vs 240V is slightly less dangerous to humans. It probably makes a bigger difference in equipment and wiring faults due to Ohm's Law. (Double the voltage double the current; thus 4x the power).
Note that although the US is a 240V country, nothing is more than 120V to earth. This an approach the British took with construction-site 110V power, where each "leg" is 55V to earth.
We are concerned with series arc faults (arcing across a loose connection in series with the load) more than Europe is; since our 120V appliances take twice the current for the same job, series arcing makes twice the heat.
European power is distributed to the poletop as 3-phase 400V "wye" with 230V phase-neutral. 1 to 3 phases are delivered to each home.
If you add 20% to that, consider what you get: 480V 3-phase with 277V phase-neutral. That is exactly what USA industrial power is. Culturally, it is treated with fear and respect - here's a 277/480V arc flash... Electricians are not as quick to work "live" in a 277/480V panel. The major difference is the presence of "whole-house RCD" to protect most parts of the system in a European house.
* Normally our 240V breakers appear like two singles handle-tied. They aren't. Actually there's an internal mechanism for "common trip", the handle ties are merely decoration / to remind a maintainer that both must be thrown.
** Originally, 120V (well, 100V then) was only for lighting and 200V for everything else. But then, they provided receptacles/sockets for desk and floor lamps, and then people plugged radios into them, and then things got out of hand. We have a 240V plug standard (NEMA 2 and NEMA 6); we really ought to start using it so we can have fast kettles.
GFCI vs RCD
In Europe, they use a "whole house RCD" to detect leakage currents (current drawn by house does not match current returning). This is a compromise system with a number of priorities: detect ground faults that threaten equipment, provide limited personnel protection, stop parallel arc faults (arcing live-earth or neutral-earth that is not sufficient to trip an overcurrent fuse or breaker), and do this economically at a whole-house level. The technology at the time favored RCD, as digital signal processing was not yet ready.
The ideal detection threshold for human protection is 5 mA of leakage. However, a whole house has ordinary current leakage that is not a threat and is unavoidable (not least: electrical cables have capacitance) which is higher than that. Europeans and Americans took different tacks to this dilemma.
In Europe, the opportunity to protect the whole house was seen as worth exchanging for somewhat less human protection. So a 30 mA threshold was chosen.
The United States came around slowly, and placed human protection first. As such, "5 mA threshold" was not negotiable, and they traded away the opportunity to protect the whole house.*** So the protection is applied on a per-circuit basis with some length limitations. And this results in most circuits not being protected, except on the most modern houses where most circuits are protected by use of many xFCI breakers.
When the U.S. finally came around to dealing with arc faults, more modern tech was available, such as digital signal processors to actually "listen to" the electrical waveform on the wire for the pattern ("sound") of arc faults. That crinkle-crunch sound you get hooking up speakers live is the sound of an arc fault. Most of those AFCIs include RCD/GF detection as a way detect L-E and N-E parallel arc faults. However they use the 30mA sensitivity.
*** Keep in mind, American services are enormous. A typical main breaker is 200A on a single (split) phase. Compare with a German home with 64A main breaker x 3 phases. But you can see where an RCD detect coil with 3-wire 200A going through it would be a beast. It probably wouldn't fit in any of our breaker casings!
Our sockets
For those who fear our sockets, placing the circuit under GFCI protection is a near "golden bullet" for this problem and many others. You can also enhance safety by installing the sockets ground up, so if a metal thing falls in the gap, it will land on the ground first. (Assuring contact with it and any other pin will result in immediate GFCI trip).
Remember our GFCIs are 5mA-rated for full human safety protection, unlike the 30mA compromise system used in 230V-land. 10mA can stun, and a stun is a kill if water or ladders are involved.
The UK plug is a handful, and while the fuse is nice, our appliances are rated by UL to fail reasonably, i.e. trip any circuit breaker they're allowed on before bursting into flame. This is also why using the correct breaker is required; if Article 230 motor rules allow a 35A breaker on a 16A motor load but UL says only 25, it is because UL believes a 30A breaker would not trip soon enough.