Yes, but a public charger is going to be, a) busy and have queues and b) take a decent amount of time.
I'm going to use Wellington here as an example, but if I lived in Mt Victoria, Mt Cook or Newtown, chances are my car will be parked curbside. Due to these suburbs close proximity to the CBD I could either walk or cycle to work. If the car is only being used weekends, the last thing I want to be doing is spending 30-40 minutes charging the car before I can go anywhere.
They're not going to be that busy because the majority of people charge at home.
Right now, the edge cases where someone has no means of charging at home and only uses their car on the weekend aren't catered for with an EV. That's not to say that it will always be this way. There's no reason street lights can't be equipped with a public charger to cater to those who park on the street, as an example. I guess the other question is, what would you be using the car for in the weekend that public transport doesn't cater for?