I agree with all that you've said about not being able to predict every situation.
I also think that carrying food and water, three days' meds, a festival poncho, torch, tissues, and a shewee will mitigate the unpleasantness of the wait for the breakdown truck to arrive in many of the situations you've mentioned, and other situations too. In the worst case, it will keep you alive until the sun next rises and you can see to walk somewhere useful. The stuff I listed is also useful if your train is delayed, the station loos are minging and you don't want to sit down, it rains unexpectedly, or you simply need to blow your nose.
Refusing to carry anything at all, as some posters have stated, is just as daft as carrying a 70l rucksack containing boots and jump leads just in case your taxi breaks down. You need to balance the inconvenience of carrying the item with the likelihood of an incident where you'd need it and the impact of not having it.
Or you were on your way to collect your next prescription and you were delayed, but you had an extra strip of tablets in the medicine cabinet that you saw that morning you'd have brought if you'd have known.
I sure I mentioned carrying three days' meds in my original list. The small size of prescription medication and the serious impact of not having it makes it a no-brainer to carry it routinely.