And lo, there is verily even more information presented in the video than this thread has yet revealed. For what Alec says in the video is that this purge-the-cold-water advice is specific to North America, and he even explains the reasons why!
In which case my comment still stands for those who also haven’t watched the whole video, which is probably a fair amount of people
His argument is that appliance manufacturers are trying to simplify their lineup by making models that would work in homes without a dedicated circuit (15 or 20 amp). Although I can't think of a better argument that still doesn't quite sound right to me. The NEC has required dedicated circuits for dishwashers for quite a while now and IIRC that requirement has been for a 20 amp circuit for a few decades. Even though you typically only see 15 amp receptacles, kitchens have required 20 amp circuits for somewhere north of forty years.
I think a lot of his video is simply based on testing with crappy Whirlpool and AEG dishwashers. There's a reason why Bosch (and these days LG) dishwashers are pretty much universally recommended.
For example in Australia a standard house circuit is 10 Amps, but because it's at 240V we can get 2400 Watts (realistically more like 2300) out of a _standard_ wall outlet that is in every room of your house.
The electrical code (NEC) has started moving towards requiring 20 amp circuits in other rooms and more 20 amp circuits in kitchens.
a.) I'm going to go out on a limb and suggest that most countries will place limits similar to the NEC's 80% rule.
b.) There are other high current draw devices in a dishwasher that will have to run concurrently like the water pumps.
Same with things like electric kettles. You're not going to find 1,800 watt kettles in the US even though they're designed for circuits rated at that. A quick peek at the kettles available in Australia show that most top out at 2,200 watts for the same reasons.
In the context of a dishwasher 240V would only get you more powerful heaters than you could run in the US if the circuits were rated at more than 10 amps. Voltage isn't the issue.
A UK circuit on the other hand would fix everything. It has the same number of amps (or maybe more), but double the voltage.
The problem isn't purely amps or volts, but in general home circuits tend to have a similar number of amps, and higher power usually goes hand in hand with higher voltage. That's the sense in which voltage fixes the problem. A US appliance staying well within amp limits has a lot less power than a UK appliance staying well within amp limits.
Your standard home has a supply of 3 phase power @ 35A (southern Germany) or 63A (northern and western Germany), I think only the former GDR is at standard 3x25A, because like in many former Communist countries they had to save on expensive copper and aluminium, and since a lot of the GDR was heated by steam-based central district heating systems, you didn't need that much power anyway.