Big Mom's request was nothing short of blatant robbery. The commercial district of Shapodi Archipelago was almost invaluable, as it was the necessary route for pirates heading to the New World.
Pirates belong to a dangerous profession. Although their income is unstable, it is very high, and they basically do not know any restraint.
Wanting to hold an auction in Shapodi, mere force is not enough. None of the Four Emperors have any open industries on Shapodi Archipelago, not because they don't want to, but because it's fundamentally impossible.
Shapodi Archipelago is very close to the Navy Headquarters and not far from the Red Soil Continent. It's within reach of the World Government and Navy.
