I really don't think there is an answer to that question, moving 50K people anywhere is a huge task, it's never easy, given time will get easier but it won't ever be simple to get in and out. You'll find that plenty of people will hang around after the game for a few drinks at the ground, others will go to nearby pubs others to that marquee across the road, others walking back into town others on busses you're never going to get 53K people stampeding towards sandhills.
Yes, it is always difficult to get these large numbers of people to and (particulary) away from any stadium. That is why site choice is an essential part of the process, because creating that type of infrastructure at a poorly sited venue can be more expensive than the stadium itself.
That ease of movement is entirely dependent on the number of available routes serving the vicinity and their (excess) capacities, aswell as the amount of public transport provision that serves the site, and how much of the fanbase/customer-base has access to direct-services to that site, because public transport can move far more people, more efficiently than cars. Hence the desire to be as close to the city-centre as possible, which generally copes with equivalent or larger people-movements every rush hour, and often much larger numbers when the city hosts special events etc.
Proximity to the city centre was continually highlighted as one of the key selling points for BMD. However, this disguised the obvious fact that apart from the Northern line nearby, the site itself is in a public transport blindspot, with very limited road access and probably right at the limit of "convenient" walking distance to/from those transport hubs/networks.
I think there are solutions to bridge that gap between the site and the city centre, but as the transport plan clearly states, that requires a complete reversal in the proportions of fans using public transport/walking to the stadium as opposed to cars. If we don't fully embrace that, and that modal-shift is not achieved, then the site will be gridlocked, as was seen at times for the 2nd event, at less than half-capacity.