Weather is one major reason. In Florida, it basically never stays below freezing for longer than a day. So the water stays water.
In Baikanour, it can be quite cold for long periods of time. If you tried a water suppression system in the midst of winter in Baikanour, odds are good you will have to wait for spring to use your launch pad again, as all the ice forms so thick you cannot get it off without destroying the pad.
Florida also is somewhat lacking in natural or even unnatural cliffs. Something of a flat place. Sure you could build one, and in some ways, they did for LC-39A/B where they drive the Shuttle/Saturn V (Soon to be Falcon 9/Falcon Heavy) up a manmade ramp to a man made elevated platform so that the thrust can go down below. While the scale of the platform is quite large, it is nothing quite like what the Baikanour cliffs are like.