Why American battleships carried lattice masts

Why did American ships use large lattice or cage masts?

Designers expected the lattice structure to remain stable after shell damage, but it did not perform as hoped.

Designers expected cage-like lattice masts to be stable and strong and to remain useful after shell damage. The assessment here is that they failed to deliver those advantages. Their intended resistance to damage explains the design's attraction, despite its disappointing performance.