The people who think it will strain the grid probably live in California. Pretty sure trying to blow dry your hair is enough to cause a brownout over there if it's not off peak.
But yeah if I had an EV I'd probably use the level 1 charger most of the time overnight. On days off in the day time I'd plug into the solar outlet. I'd probably look at adding more solar panels too. Don't really have a good spot though. House roof is too hard to reach with a long pole to take the snow off. But I'd try to figure out something.
What I can see maybe putting a strain on the grid is super chargers, if there are like 10 of them in one spot, you could be looking at over 1mw of power potentially. I assume the hydro company would just give those places their own substation transformer off a high voltage transmission line though.
It's always possible to upgrade transmission and even distribution lines to higher voltage too which allows for more wattage at it's amp capacity. That does require changing out all the transformers on that line though so it's not an easy job.