You have no working model of a civilization yet you think its behavior can be predicted mathematically. K.

Bigger fleets need more fuel, munitions, maintenance. Labor and materials that they have to bring along.

Rational by our standards or by theirs?

You also demonstrate no knowledge of tactics or military strategy, yet you find battles predictable? K.

It protects the colony because they have the capability to build their own fleets, munitions, bases, replace losses, etc. Advantage goes to the ones with the closest support and resources. The colonists also see the Imperial fleet coming, so they'll have time to prepare extensive defenses.

The literal definition of a Kardashev 3 society is one unified civilization controlling all of a galaxy's energy output.