As far as I know, the only plants that might suffer from an extremely low KH (low carbonate concentration) would be carbonate eating plants like vals. Generally speaking low to near zero KH isn't a problem.
People used to believe that low KH would lead to pH crash, but it doesn't. The inability of CO2 to dissolve in water beyond a certain ppm stops the pH from ever getting below 4.5 or so (at typical aquarium water temperatures.) That is not low enough to harm anything. And, long before reaching that pH, the fish would suffocate from the CO2 that is lowering the pH.