Electric Vehicles

That… applies for fuel too? If it’s not super busy, I’ll go inside and grab a snack while getting fuel.

That's illegal here, the hose is not allowed to be able to lock.

That’s got to cause more problems than it solves.

Just because you don't see how it can work, doesn't mean it doesn't. ( argument from ignorance ) First of all the grid of Estonia isn't isolated, it is connected to a much larger European grid of about 700 million people.
I know this is pretty recent, before it was connected to Russia. But these connections are strategic and are constantly expanded throughout Europe.

These 1.5 MW chargers are generally connected in groups, if the grid isn't powerful enough to handle them, they will not be established.
But my guess is they use batteries to store power for fast discharge, that are charged a steady but lower rate.
Remember when a car charges at that rate it only draws power for 5 minutes. So one charger can handle maybe 12 cars per hour.

Here in Denmark we have Charging stations where multiple brands are represented, with each their "island" of chargers. And I've seen some that have more than 20 stations with 400 kW charging available. The reason they aren't bigger, is that there isn't a market for it yet. But if they are run all of them simultaneously that would be 8 MW.
But if 2 on the same station are used at the same time they only provide half the power. So the max is really only 4 MW.
This is in Denmark where we are about 6 million people, and our peak AFAIK is only 5,3 GW, But the country is split into 2 energy zones, East and West, so for one zone the number is probably closer to 2,7 GW. Mostly half the country is on 1 island, and the rest is mostly a peninsula and an island.
So closer to 3 million, and for some reason with way lower peak power per capita than Estonia. But the electric grid is connected to Norway, Sweden, Germany, and even UK and Poland.

IDK how they do it, but it works, and I've never experienced a problem.