Statistical algorithms always make more concrete assumptions of the signal. DFT / Fourier transforms are great as they are a direct mathematical operation, that maps neatly to (basic) equations. There's a lot you can do, and easily grok, with FTs. Once you get statistical, a lot of things are harder :)
If you want pure performance, and understand the underlying statistical processes, then sure I totally agree with you.
You can even use these algorithms with a single snapshot (spatial smoothing).