Actually the ideal location is right in the middle of things.... and when space is available that is the trend for stadium planners. If possible they'll even shoehorn them into the middle of downtown city blocks with no parking.
I pass the site daily. The point is, far fewer people would need to drive. As public transport capacity is easily the highest for the whole city region in the centre. That capacity drops exponentially with distance from town. BMD currently enjoys practically no regular services. The whole of the south docks have enjoyed substantial redevelopment over the last 30yrs but it has barely merited a single new bus service. If Liverpool waters grows to the extent of the orginal scheme we may get a station at vauxhall and a dedicated bus route or two..... but that will always be a tiny fraction of that available at the more central Kings Dock.
People will always want to drive for a variety of reasons, it's not a case of not having to.
Sandhills is not that far away, certainly no further than say Liverpool Central to KD but you can easily run shuttle buses from Sandhills with loads of room to do so anyway. The South Docks have not had a massive high profile stadium put in the middle of it, of course there will be additional bus routes, there is nothing to stop that happening there.
Kings Dock isn't even central anyway. It is on the periphery of the city centre.
Kings Dock would have been fine, so to will BMD. The past doesn't matter anyway now.