Uncertainty makes people anxious. In an ICE you can be certain that you will be able to fill your car up and it won't add any significant time to your journey (except for that one week last year with the panic buying). With an EV you can't be certain you will find a charger where you want one to be. I travel to my sister's which is just over 200 miles away. I can't charge at their house and we often go out for the day while we are there which means I have to stop for a significant amount of time on the way down so I have enough for the weekend and to get me back to a charger on the way back to get another full charge on the return. We have young kids so we travel on a Friday night after work so an extra stop for an hour is a massive inconvenience. Pulling in somewhere to stop for food (which we never used to do pre-EV) only to find that there are no chargers is a pain in the ****. Because we need to charge near our destination means stopping to eat at 9pm instead of the time you would actually want to stop to eat or two stops.
All these things cause anxiety. You can call it range anxiety or not but that is irrelevant. Owning an EV can be incredibly inconvenient and being a Tesla driver with the supercharger network and no kids means you aren't representative of all EV drivers so stop telling people that it's all sunshine and rainbows. EVs can be great and massive pains in the ****.
Lack of understanding and fearmongering makes people anxious too.
We've had a fuel shortage a few times, or panic buying in the last few years haven't we? Don't want to fearmonger, but these may become more common too, as we demand less fuel and as the supply of it is reliant on morons.
If I'm going to an area where there's a lack of charger choice on route, or nothing at the destination I would just stop sooner, but for much less time and rely on zap map. I've had zero instances where a charger broke, or wasn't avialible when I got there and there wasn't a free alternative. Like I say though, I like most don't need to rely on public chargers much, and the plug at home is more relaible than any car fuel source.
Your example is a bit of a one-off/ extreme though isn't it? How many people do this/ how many times a year? A drive 200 miles/ 4 hours with kids seemingly where you don't want to stop, and then having to drive again all weekend, when you get there, to places wiht no chargers seems a bit rough on you all to be fair, you especially. That 200 miles is on the verge of where most would try and push through without stopping though, which is what I used to do, and get stressed. Now I would just stop at 150 and top up to 80% in half an hour, and do the same on the way back. I'd stop on the way down in an ICE now too. Funny thing is I do similar EV trips to the southwest, 300 miles, but because it's a longer drive, the stop is expected anyway. Still only works out 1.5 hrs total charging/ stops mind. Seems like we're visiting there often (missus parents), but it's actually only a few times a year. This ends up being 90% of my total EV public charger use.
I don't drive a Tesla, but I've had a 200 range car and now a 250, both using CCS and never used a Tesla supercharger, I don't see what the problem is in the UK.
There are still plenty of 100kW+ chargers, image bleow, and three times as many more 50-100 and most cars wouldn't be drawing more than 75-100 for much time anyway, the 50-100 chargers aren't much worse in reality, and often suit where you want to stop better.
Sure there are some rare 3-4/10 inconveniences (or rethinking) with an EV, but for most there a hell of a lot more 1-2/10 ICE inconveniences, which add up to a hell of a lot more, and that's only fuelling. Not all ICE's have 500 mile tanks either, most cars are closer to 300.
Again though, only basing this on 200+ range cars, home charging and ~12k miles a year, but that covers most people in the market for newer cars I expect.