There's nothing worse than travelling to a holiday vacation spot to find out the only rental options are those heavy plastic or aluminum paddles with nearly straight angled blades.
Break down paddles are also a wise choice to carry with you on an expedition. You can tuck them under your deck tie-downs or stuff them in a backpack. Carrying two piece kayak paddles is also a good idea if you get tired of standing and/or need to sit for a long upwind paddle. I've interviewed several expedition paddlers who have broken paddles on trips. It does happen.
There's several companies that make 2 piece break down SUP paddles, but few make a 3 piece paddle. Here's a few (not all) options...
Werner's Fuse, Carve, Advantage, and Nitro.
Imagine Surf's Rapier Paddle.