Well you can down vote me all you want but it's not a UX problem that's been solved so far and it's a legitimate factor in range anxiety.
Unlike switching the lights off you have to get out of the car to plug it in.
If the car is going to beep before you get out then it's not a reminder for something I've forgotten,as with lights left on, it's just irritating UX noise, like the "don't forget your mobile phone" message. After a very short time I go blind to that.
If it's an alarm on a mobile/smart watch it's still a tedious chore to have to plug in a car when it's raining or I'm in a rush or I've parked in a spot without a charge point.
People _will_ forget to charge their cars, just as they forget to charge their phones and they will be late because of it.
If purely electric cars are to be brilliantly convenient everyday repacements for fossil fuels they'd be better with either some kind of induction charging, fast charging that doesn't take hours or hydrogen fuel cells.
If we had better ways of splitting hydrogen we could "fast charge" anywhere water and electricity is available.
But no, it's not a huge issue. New cars seem to come with apps nowadays, so as you said your car can just send you a notification to your phone if you haven't plugged it in five minutes after arriving back home. And maybe another one if it's still not plugged in before you go to bed.
Unavailability of charging (see sibling comment) is a bigger issue that won't be as easy to tackle. But reminding users to charge their car isn't what's hindering EV adoption. You can be late if you forget to fill up your petrol car, too. That can easily take ten minutes if there's a bit of a queue.
