It was clear from the start that this site was always going to be anti-car..... the stated required modal shift to public transport was a dramatic one, which appears to have gone over the heads of many drivers.
The issue then, being that it was also a bit of a public transport blindspot, unless you had direct access to Merseyrail (which only approx 20% of the local population do), which in turn was limited by station and line capacity. Proper marshalling increases the station capacity, but line capacity is pretty much fixed until signalling and other infrastructure is added.
The saving grace in terms of public transport is supposed to be proximity to the city centre and all of the public transport capacity there. However, at one mile just to the edge of the city centre (further to bus/train stations).... it is at the very edge of the reasonable walking envelope. Therefore, it is important for the shuttle bus service to be as efficient as possible, to essentially drag the site into the city centre. Allowing the vast majority to leave their cars at home. Of course, if that doesn't happen and the few access routes are choked with cars trying to park as close to the stadium as possible.... then the Shuttle buses cannot work. A transport catch-22.
The hope is that the Liverpool Waters, Ten Streets and other schemes linking the site to the city centre will prompt more hard-wired and fully segregated public transport very soon.