Surely the reason for the 'south-eastern bias' in non-league football is that outside London it has very few league clubs compared to the north and to a lesser extent the midlands. Look at Lancashire and Yorkshire, and then compare them with Essex, Hampshire, Hertfordshire, Kent, Surrey and Sussex and you will see what I mean. This is probably because there were never many cotton mills, coal mines or iron and steel works and their accompanying cities in the home counties either.
But they have always been full of what were once amateur clubs and their leagues. When I was growing up there was a kind of pyramid - Isthmian, Athenian, Corinthian, Delphian -but with no promotion or relegation. You moved 'up' when an Isthmian League club, e.g. Wimbledon, joined the semi-professional Southern League, or when the Isthmian League decided to expand with the arrival of floodlights.
Meanwhile, as far as I remember, the only equivalent in the north was the Northern League of Bishop Auckland, Consett, Crook Town, Willington etc, which was in effect a north-east league. In much of the north there simply wasn't room for the kind of set-up that existed in the south-east. And, as Sean of the Shed's post suggests, the legacy of those days lives on.