Most people don't realize that BEVs (not hybrids) have batteries large enough to last a whole week of commuting. This gives a lot of flexibility in when and where they can be charged.
They're typically configured to charge overnight, when charging speed doesn't matter, and electricity demand is low (if the demand shifts, they could be configured to charge at different times, e.g. when they're parked at work). EVs are designed to be left charging unattended, so they can just be left plugged in whenever they're parked. That's a different use-case than quarter-megawatt chargers for road trips.
New cars have vehicle-to-load capability built-in already, and there are trials to use them as grid storage. The more EVs there are, the more they can be used to shift renewable energy and flatten the duck curve. EVs can help the grid, not strain it.
Large fast charging sites for road trips typically have their own batteries, because it allows them to have cheaper lower-power connection to the grid, do price arbitrage, and use their own renewables. This is also a place where degraded batteries from old EVs can be reused.
Of course the electric grid will need to be expanded. Lament about that sounds like developed countries have forgotten how to develop infrastructure?