FPS is one way to convey the total picture that is kinetic energy.
Physics dictates that all else being equal, the more energy you can put into something, the more work it can do. In this case, if there's a significant difference in FPS between two otherwise identically equal guns firing identical ammunition in identical environment, the gun with the higher FPS will definitely have an advantage in shorter time-on-target (less lead needed against moving target), greater energy delivered to the target (to ensure the hit is felt or heard), and likely have an advantage of greater overall range as well.
So simply claiming that FPS doesn't matter really doesn't reflect the reality of the science involved. FPS isn't the most important factor, but it also sure isn't a non-factor.
"The Bird of Hermes is My Name, Eating My Wings to Make Me Tame."