IMHO, one easy way to think of chain catenary is this: When you need it, it won't be there. With enough wind, the angle of pull on the anchor will be the same for chain and rope.
If you are concerned, then anchor with enough scope (chain or rope) so the "lifted shank angle" is still significantly less than the shank-to-fluke angle. That way the flukes aren't getting torqued out of the bottom sand or mud.
Where we anchor in 10 feet of water (roller is 5' over the water, sand bottom), I really like 115 feet of chain on one anchor (60 lb Manson Supreme), 75 feet of rope & 30 feet of chain on the second anchor (40 lb Bruce), snubber on the chain, and a riding sail to keep the boat from tacking (5 degrees versus 120 degrees). Winds have hit 70 mph in a passing storm. I use the second anchor if we are going to be away from the boat for awhile. The Manson is set at 1,500 rpm for 10 minutes. (We previously used a 60 lb CQR. 1,200 rpm would set it, but 1,300 rpm would break it out every
The one time this past summer when the Manson didn't set, having all-chain and an electric windlass meant it took less than 10 minutes to easily raise the anchor, motor forward, and try again. When soloing, it also means I don't have to leave the helm after departure, to coil the rope back into the anchor locker.