T̶h̶e̶ ̶b̶i̶g̶g̶e̶r̶ ̶t̶h̶e̶ ̶c̶o̶u̶n̶t̶r̶y̶ The more shipments you have, the more officers you need. The more officers you have, the better the chance one of them is working for organized crime.
Although, your number of entry points should scale like your perimeter, while your population to pull agents from should scale like your area, so unless you have a very weird geometry this should get easier as you increase in size, right?
The main factor is the quantity of goods which need to be inspected, and that tends to scale with the population which is buying the goods.
> your number of entry points should scale like your perimeter
Is that really true? An entry-point is generally something the people choose to create to satisfy the pre-existing need to transport goods, by building roads, rail, harbor-piers, etc.
Border-checkpoint facilities don't spontaneously generate in trackless wilderness or barren coastlines, like some fantasy-dungeon that the Adventurers' Guild must periodically raid in to avert a stampede of monsters.
Airports not included.