Does it mean bookies do not want big exposure in smaller leagues because there is a higher possibility of rigging, or is it just because the betting volume is smaller compared to major leagues?
Your instinct is right in this because it could be due to the reasons you speculated and that revolves around low bet volume,market inefficiency, risk or possibility of rigging.
It is risk management practices in effect as you noticed this because these sportsbook are in the business to make money, not to lose it.
Hence how they know how vulnerable they are when it involves local leagues and why they try to minimize their loss on every game. Whereas for major leagues it's the opposite because the house is confident enough to take the big risk.