In the absence of coral or rock, I think it is true that you don't need chain, with emphasis on the word need.
Probably most boats under 32 feet in soft bottom, brown water areas, use mostly rope, and we don't hear a lot about chafe. The risk we hear most about is wrapping the rode around the keel (either tide or current can do that), and that is solvable with smart use of a kellet.
The bigger the boat the greater the risk of chafe. Small boats have limited rode pressure against rocks, larger boats have much greater cutting force. In my case, I use over-sized 1/2-inch nylon, because I had it and because it is easier to grip than the 3/8-inch the boat actually needs. And it also reduces my cutting risk disproportionatly, because there is more to cut and because the spot-pressure on a rock is lower. I also like the reduced stretch (no bungee).
Some anchors like chain for the initial bite when setting. Not pivoting fluke anchors, which often do better with no chain in soft mud. But it doesn't take much. 10 feet is enough for that. I've used all manner of old-style and new generation anchors with little or no chain. My fortress kedge on my cruising cat had no chain (easier to row out). It did have a covered Dyneema chafe leader.
Boats with rope swing more. This depends on the boat; a multihull on a bridle doesn't swing because of the wide bridle. You can use a riding sail, kellet, or hammerlock as well.
With chain you can anchor in less space... until it really starts to blow (>60 knots). Then I'm not so sure it matters.
And finally there is catenary. It helps, but so does nylon and more scope. With rope you will have to use slightly more scope. For example, when 3:1 might work with chain, you will need 5:1 with rope. When it blows rope rode users got to long scope sooner, but once we get out to 12:1, there is no difference.
Is chain good? Yes, it solves a lot of problems. The anchor sits a little more quietly. The windlass likes chain. Do you always need it? No. Is it easier to live with on may boats? Yes. Either can work, if you know the rules. Horses for courses.
[I've cruised with all-chain and with only 6 feet of chain.