🚗 Why are our cities (usually) flooded with cars?

In a nutshell: The economics of parking lots

During the summertime, there are many empty parking lots in the street where I live (Prenzlauer Berg, Berlin). People are on vacation and out of town. During the rest of the year, it is not so. Parking space is scarce. The city is overcrowded with parked (and also driving) cars. We got used to the fact that cars are everywhere in cities. Right and left on every roadside - cars, cars, cars. We shouldn't have gotten used to it. If market rules were applied for parking spaces, there would be far fewer cars. Here is why.

Parking lots are - in economic terms - private goods. Most of all, private goods are rivalrous and excludable. This means that ownership can be restricted to a group or individual (excludable), and such a good can only be used or consumed by one party at a time (rivalrous). For example, dinner at a restaurant, grocery shopping, aeroplane rides, cellphones and parking lots - they all are private goods. 

It is generally accepted among economists that private goods don't need government intervention. Yet, municipalities provide parking space. Even more, in most cases, they give it to their residents for free or for just a small fee. 

What would our streets look like if parking was a private matter? If one had to rent space for his or her car like they have to rent a roof over their head? - Why do we have to pay for where we live but not for where our cars stay? 

If there was a market for parking space, parking in cities would be more expensive. Therefore there would be fewer (parked) cars. Therefore there would be more space for people. For playing, restaurant tables outside and opportunities for the municipality to create nice common places. I would be happy. 

Notes

Private good definition: https://www.investopedia.com/terms/p/private-good.asp