It is the only uninterrupted motorway from the east to west sides of Melbourne, but not the only core arterial. There are other roads you can use to get from one side of town to the other. A lot of traffic using the tunnels is just commuter traffic from the east anyway.

The tunnels never were public roads, they didn't exist. You can still drive on pretty much the entire length of the West Gate Freeway, right up to the tunnel portals without paying tolls. There are some short sections of motorway though that were previously un-tolled but are now tolled, though there has been some pretty extensive upgrades.

That said I'm no way in favour of City Link, but the real core 'arterial' for urban commuting is our public transport system. :-)