What is the difference, in terms of build quality and components, between chargers with the same number of ports but with different power?
Build quality is independent of power output in the range you are discussing.
The double-the-current power supply will deliver double the power as Power = V x I and V is the same in both cases (or should be). (Nominally 1.2A x 5V = 6 Watt and 2.4A x 5V = 12 Watt.
The 12W supply is designed to produce a higher wattage output. That may seem obvious but may not be. If frequency of switching is the same this involves
In resistive areas of the circuit power is proportional to I^2R so doubling current MAY double power dissipation.
Assume that all components are sized to be just-about-right for their tasks
In practice this is often not true - convenience and minimal cost differences between differently rated components and economies of scale and stocking convenience often results in a part being used which exceeds requirements. eg 1N4001...7 diodes used to be the industry standard through hole 1A low frequency power diode of choice. A 1N4001 diode is rated at 1A, 50V. A 1N4007 is rated at 1A, 1000V. the whole ...2 3 4 5 6 range in between exists BUT in practice you MAY almost always only ever see 1N4001, 1N4003 and 1N4007. I'd never use 1N4001 and a 1N4007 MAY be cheaper than a 1N4003. In days of yore I'd just stock 1N4007 and never need to choose.
But, assume that all components are sized to be just-about-right for their tasks
The higher input current and power will require
Higher current rated switching transistor(s) or ICs.
Double current rated diodes in AC mains bridge and in high frequency output diode(s) or if synchronous rectification is used, more capable MOSFET synchronous rectifier FET.
High frequency transformer core able to handle double the saturation current so morecore material and thicker wire.
Carried to extremes, greater copper area in tracks, better cooling, ...
Higher ripple current capacitors.
In practice the differences in a 1.2A and 2.4A supply will be small or absent in many cases.
If a switching MOSFET is used it MAY be the same.
If an IC with an integrated high voltage switch is used it will probably be more highly power rated as cost and power tend to be more correlated than for MOSFETS.
And more ... . As power levels get up there are more differences. eg a 10A and 20A supply will almost certainlyt use different diodes and MOSFETS and transformer core size will probably be substantially different and ... .
It is possible, particularly if the device is self-powered. Attempting to draw too much current or even a dead short will not hurt a proper USB host port. However, accidentally applying high voltage to either of the data lines could be bad. At least that could blow out the drivers for that port, but it's no stretch to imagine it could take out the whole hub chip.
This is not a place where fuses are reasonable and would do anything useful anyway. By the time a normal thermal fuse trips, the hub chip will be long dead. Putting anything else in series with these lines is a problem since they have to carry high speed signals. The hub chip will have protection diodes or similar to power and ground. That will protect against the occasional static discharge. Protecting against anything more than that would be expensive and not worth the extra money for the very rare case it saves something. It makes no sense to waste even a few pennies protecting a $50 motherboard when this protection will only matter once in every 10,000 cases.
You can't apply line power to the audio jack, the video output, and most other external connection points of a PC. I don't see why USB should be singled out for extra and burdensome protection.
Best Answer
For the same reason that many devices ignore the requirement to enumerate and ask for more than 100mA of current.. because they can get away with it (most ports will work okay even with a big capacitor on there) and since there are lots of devices that ignore the 10uF limitation, then the computer designers have to make their ports work or face a lot of complaints from users about their crappy USB toys not working.
Your assumption that these work "without any problems" may not be correct. They could have problems with a minority of available host ports and not be overly concerned about that.