I have experienced both sides, my original pond the koi destroyed any plants that touched the water in their pond. I ended up building a separate pond for plants that fed into the koi pond, similar to what sissy mentioned.
My current pond (10,000 gallons) built once I moved is loaded with plants and has koi in it. In this pond there were no large koi in the pond initially for the first year or so, and I let the plants pretty much grow bare root in planting beds of pea gravel. So the plants pretty much became well established before the koi in the pond attained any size. Also, I have water celery growing around the rock edge of pretty much the entire pond, which the koi love to eat, but that stuff grows like wildfire, so they can’t eradicate even though they try. Currently, have a lotus, 3 different lilies in the pond that the koi leave alone. Don’t know if it’s the size of the pond or the fact that I let the plants grow like crazy for the first couple years before there were any large koi in the pond that made the difference.