That's one option of course, though I prefer a cap and trade system on permits to operate a vehicle in those zones, reducing the cap as much as possible. People in city centers are less likely to own cars as it is. Often, road infrastructure (especially parking infrastructure) exists to benefit the suburbanites at the expense of the city dweller.
The UK is a largely rural country. Living in z1 and owning a car in order to get out of the city and travel freely is perfectly reasonable. There are also many pursuits and personal and familial reasons to make use of a vehicle.
It is also not reasonable in any way to charge persons to leave their homes (currently the case anyway). That's morally repugnant.
The infrastructure to connect your house to the public street network has to built and paid for by someone. It is the same for other types of infrastructure such as gas and electricity. Do you think it morally repugnant to charge people to connect their house to those networks?
The same could be said for keeping a helicopter in z1, but obviously that would be silly.
I live in a far more rural country than your own (Ireland) and Dublin city centre is choking on suburbanites' cars and hgv's. Those same suburbanites vote down any cycling improvements in the council. I think it's morally repugnant that I'd be terrified to let my kid ride a bike to school so you can have easier motoring, and expect me to pay for it to boot!
I ended up leaving Dublin in the end, bitter at its catastrophically weak approach to cycling and tired of drivers being jerks on the quays.