Yoga != stretching, though it incorporates stretching foundations.

Yoga includes a lot of other things, like isometric strength, strength at ends of range of motion, breathwork, and more.

I highly encourage yoga - however, 'stretching' on its own can open up the door to injuries if you're not properly warmed up.

I rock climb, and yoga is a fantastic way to counter the 'damage' done from climbing, so I generally agree with you!