Higher rates affects only people living in Auckland, but fuel tax can get people visiting as well. Plus, I would suspect the thinking was if you can't afford the fuel tax you can take a bus. Obviously the reality is different, but that was probably the intention.
If you listened to the Wayne Brown, there was hundreds of millions of dollars already allocated for roading and transport projects. It hand't all been spent yet because contracts had been signed but work hadn't started yet. As he said, all removing the regional fuel tax does is get rid of these projects, because he will not raise rates.
Full disclosure, this is the very first time I've agreed with anything he's said.
The other option is, of course, road tolls. His argument was this is a tool to reduce congestion (I find this dubious, but regardless), not to generate revenue for the council. And I'll be honest, I find little difference between a fuel tax and a road toll - both are regressive taxes and affect lower income earners more.
In my opinion, the central government needs to step in across the country and fund the shit out of infrastructure upgrades. 3 waters, but for roads and rail as well.