If street parking was banned then car parks would be built to service the demand.
This is impossible. I suggest you look at the streetmap for just a few roads in your locality. Can you identify where these giant carparks would go. Even in areas with good public transport, it cannot go everywhere.
It only appears impossible if you lack imagination.
There would be fewer privately owned vehicles because people would be helped to make transport choices which do not involve vehicle ownership. Occasional vehicle use can be filled in by car clubs and the like. Increased use of public transport leads to increased availability of public transport, and increased walking and cycling leads to better conditions for walkers and cyclists.
There are plenty of brownfield sites which can be used for the vehicles which remain, although the idle and selfish may have to get used to the idea of walking a short distance to their vehicle rather than having it at the door, occupying public space as of right. This would do no harm in a country with soaring obesity.
We can build both up and down and use creative engineering - remember that the drivers will be expecting to pay for the service as part of the cost of vehicle ownership - so we have money to spend. We can build both up and down and use automated parking systems. I've used these systems and have never had to wait more than a minute to get my vehicle back.
We can look at parking which is empty and idle when businesses are closed. And with reduced car commuting parking space would become spare and could be rented out for an income stream.
The economic benefits of eliminating street parking result from improved traffic flow. The social benefits are to people's health, wellbeing and mobility. Children's mobility would benefit especially from a safer environment to walk, cycle and play. Currently we have a generation of cildren who will die at a younger age than their parents because if they leave the house to play they find themselves nudged off the pavement to make space for an urban 4x4 driven by someone who's human rights are infringed by having to walk more than a metre to their destination.
It won't happen overnight, but a start would be made by charging car users a realistic rental for the space which their idle vehicles occupy. £30 a year isn't it. £1500 a year is far more reasonable.