This would explain the small size of Bronze Age countries. As transport technology gradually improves, we'd expect the size of countries to enlarge.
Earlier paved roads do exist,[2] but (due to their high material/labor cost) this was only sporadically feasible, between settlements with high traffic between them. Part of the genius of the Roman road network was the system of bureaucracy and taxation to pay for it. This meant that a traveller (or an army) could rely on the existence of a continuous, high-quality road linking distant locations.
[0] http://engineeringrome.org/ancient-roman-roads-and-their-inf...
[1] https://en.wikipedia.org/wiki/Roman_roads
[2] https://www.theguardian.com/science/2011/mar/15/britannia-ro...
And, it seems that this kingdom was much smaller than what one could even walk in 1 month, even if there were no roads. 30km x 25km could easily be walked in a day by a relatively fit person at a reasonable pace. So maybe it isn't just travel time, but things like whether the state has enough power to prevent banditry (correlated with distance from capital) or distance-as-measured-by-armies-and-tax-collectors.
Those distances might be doable within the developed areas of an empire when you are moving between established settlements or way points with established infrastructure but not when there is no where to rest and no where to eat.
To make it worse, a distance you can do in 1 day isn't the distance you can do every day for weeks, which has to be less. And it's always possible someone pulls an ankle or the rain comes, which will further lengthen the trip.
I believe the argument was that countries couldn't be larger than 1 month travel time. It's a maximum size limit, not a minimum.
Also as others have pointed out, I think you'd be surprised how difficult and slow it is to carry heavy army-supplying loads over a winding network of unimproved trails that periodically get flooded out or turn to mud, all while being assailed by bandits and toll collectors. Travel in that era was not only slow and expensive, but risky.