Yes it should be free, for most cities that are not at a super high density and already very over utilized in terms of traffic capacity. Having free parking improves the quality of life for most residents, enabling them to use cars to get around quickly and conveniently. It’s faster than alternatives (unless you design streets to be purposely inefficient), works in all weather conditions, and lets you move kids and things around.
Parking also helps the local economy because people are more likely to visit businesses. Small business owners often lose customers if nearby parking goes away or isn’t sufficient, and anecdotally no business owner I know has said removing parking or adding costs has helped their business.