Contrary to audiophile wisdom, crossover networks "soak up" almost no power, even when all the drivers are connected. If they did they would get hot, and if mounted in a sealed enclosure stuffed with fiberglass or wool, very hot.
Agreed. They don't soak up much power. However they do act as a bottleneck or choke and any voltage drop across the crossover means less amplifier power reaches the speaker drivers.