Its not just cities. Its towns too.
An example is Altrincham. Not only did the Trafford Centre (with free parking) suck the big name chains away, but people were put off from going because of the parking charges.
It also affected other nearby towns such as Warrington.
One of the key things about getting Altrincham back on its feet has been to try and reduce parking charges by the council. The influx of independent shops and the market are talked about a lot but parking is also key to the revival.
What is also interesting is Altrincham Tesco went through a period of trialling reducing the time you could park there to 90mins (its right by the town centre). It obviously didn't go too well and before too long it had increased to 3hrs. Obviously lots of people were going to Tesco and then walking into town because of the parking.
The Trafford Centre, Cheshire Oaks and most out of town shopping estates owe their sucess to free parking. Why would people go into town if they could park out of town for free?
These are places which aren't served well by public transport. If you want to get somewhere easily you have to drive. For a family, the bus is far more expensive.
For cities which do have public transport the key is cheap public transport being an option to reduce traffic rather than price people out.
I don't think this is new or a surprise.