I am not in speech processing, just standard multidimensional signal processing... But: I urge you to use caution, every time you hear anybody say "this is the best method"! Well, it may very well be the best for HIM and HIS problem, but there is the infamous "no-free-lunch" paradigm: you may pay a dear price with your data if you go after one particular solution stated to be best by someone. In fact: Having doubt about the use of one method means, that you have to benchmark it against some/many others and THEN you may conclude: This is my best and I do not use "mandatory" LDA...You gain an advantage by using different methods: You can use Ensemble Classification or Voting to make the most out of your data - which you can't with only one method...
It depends well on the available, methods, at moment speaker recognition system mostly uses these methods. Yes we can not make it mandatory, but a good starting point for comparing with new systems. In a sense, some time we follows the rules of crowd, as the speaker recognition community is using these methods.