That strain does not seem to be reflected in the usage, which has been in a shallow decline since the 90s. Maybe they could consider using smart demand management, which is becoming popular with a lot of utilities to move usage away from peaks and into the quieter times.
I think these tariffs are meant to encourage exactly that. Note also that there are many levels of bottlenecks. One could be in your neighborhood, if all your neighbours have EVs.
Perhaps it will work. I'm just a bit skeptical because it seems unlikely to be a widespread problem. The average driver in Sweden will only need perhaps 6 kWh per day, which at L2 means charging for 35-40 minutes. A bit of demand management from the utility and everyone in the neighborhood can get what they need without stressing the local grid. Or just knock down the rate to something inconsequential and let it trickle all night.