Well, no.
rear fog lites would not have helped ANYTHING there (or at any other occasion else)
Now
that's a wrong statement. For one thing, nobody has an alternative-universe crystal ball to tell for sure what would have happened in this case if one thing had been different (vehicles equipped with rear fog lamps). That said, rear fog lamps are known to reduce crashes, and have been since the early 1960s.
The only thing they do is that some idiots turn them on - mostly in situations where they are used wrongly, like in rain - and forget about them afterwards.
You're objecting to some drivers' misuse of rear fog lamps. That's a legitimate objection -- people should use their car's equipment correctly -- but it doesn't mean rear fog lamps are useless. By your logic, turn signals are useless because some people fail to use them, or leave them on after completing a turn or lane change. That doesn't make any sense, and neither does what you say.
The PROBLEM are drivers that
* drive too quick for the situation
* leave no distance
* and so on, insert most any error to think of
Right, and rear fog lamps aren't a magical countervail to make drivers behave better, but they do afford a longer visibility distance in bad weather. That's how they provide a safety benefit.
or even better: a "pushbutton setup" for turnig it on (no steady mechanical "switch") that kills the light, when the ignition is turned off
This requirement is already built into UN Regulation 48, which states:
6.11.7. Electrical connections
These shall be such that:
6.11.7.1. The rear fog-lamp(s) cannot be switched on unless the main beams, dipped-beams or front fog-lamps are lit;
6.11.7.2. The rear fog-lamp(s) can be switched off independently of any other lamp;
6.11.7.3. Either of the following applies:
6.11.7.3.1. The rear fog lamp(s) may continue to operate until the position lamps are switched off, and the rear fog lamp(s) shall then
remain off until deliberately switched on again;
6.11.7.3.2. A warning, at least audible, additional to the mandatory tell-tale (paragraph 6.11.8.) shall be given if the ignition is switched off or the ignition key is withdrawn and the driver's door is opened, whether the lamps in (paragraph 6.11.7.1.) are on or off, whilst the rear fog lamp switch is in the "on" position.
(boldface type added for emphasis)
This requirement is at least 8 years old now, and probably helps explain why, in your words, "the idiots keep getting less. Nowadays there are only 2-3 left on my 40 km to work in the morning that insist on using their rear fogs at the nicest winter days".