In my own limited experience in Europe, yes, it indeed can happen occasionally, especially during the holiday rush if you are travelling a popular route. I haven't found it to be much an issue in practice. You can avoid the worse of it by planning ahead, shifting your departure time a bit and carefully choosing your route as the situation evolve in regard to charger capacity.
Still, even if that happen and each of your 3 stop adds extra half-hour wait, sure you waited an extra 1 and half hours but it's not like the ICE cars are as fast on those days either. There are traffic jams, 10 min queue at petrol station, 10 minutes queue for the restrooms, 20 minutes queue for your sandwich etc. Your stop in an ICE car will be longer too.
In the end, even on those high traffic days I found the experience of travelling with an EV more enjoyable than with an ICE car.
Can I just say, as an American who moved to Europe in 2022, the lines at gas stations are crazy to see! In the US, I had never had to wait for more than 1 or perhaps 2 cars to fill up, even right off the highway. Here, waiting seems to be common from what I've seen if you're traveling on a busy weekend. My experience driving has mostly been confined to the Benelux region, so perhaps it is different elsewhere on the continent.
I do like driving over the border to save 20% on fuel prices though!
Still, even if that happen and each of your 3 stop adds extra half-hour wait, sure you waited an extra 1 and half hours but it's not like the ICE cars are as fast on those days either. There are traffic jams, 10 min queue at petrol station, 10 minutes queue for the restrooms, 20 minutes queue for your sandwich etc. Your stop in an ICE car will be longer too.
In the end, even on those high traffic days I found the experience of travelling with an EV more enjoyable than with an ICE car.