while I dont have car and use with family everywhere public transport, this is a bit too strict, it would be easier to just not allow registering car unless you own your own private parking space/garage, that would already extinguish like 80-90% of the cars and solve most of the problems plus make public parking like 10EUR/hour and people will think twice whether to use the car
currently YEARLY parking fee in Prague is like 50EUR (for one Prague district where you register) while annual public transport pass cost 150EUR, what a joke, that's one way to discourage people from using public transport, at very least parking fee should cost at minimum same as public transport, where you can't buy some shared family pass, but each member of family has to cough up 150EUR, kids over 15 like 75EUR, so if you have two teenagers it will cost your family 450EUR compared to 50EUR for car all of you can share