Are you out to specifically be obtuse? Or are you genuinely not clear on methods of training? Given your supposed background I thought this constitutes a deliberately provocative question.
Regardless...
The training systems and methods as far as I can tell have not altered any great deal with the more common usage of power meters, rather they allow a means to qualify and record data that previously was either unknown or guessed at, and consequently allow for a more definitive structure to be brought to training.
A similar question could have been asked with the arising use of HR monitors many years back as opposed to working on perceived rate of exertion. Is there any evidence that training with a timing device is superior to PRE?
Given the rather complex nature of human beings there could be no way of ever proving that one "system" is superior to any other. As one other person had already mentioned psychology plays such a huge part in performance that no study could "prove" the best training system. If they could have proved it, they would have by now.
Though one does have to wonder why all these professional teams are using PMs, no? Must be something worthwhile with all that data they are collecting. Bragging rights? Must be it, no other application could be made. "I know your guy won the race but check this wattage out!"
For me a power meter allows another set of data that can be analyzed and helps in many regards to make things simpler when it comes to training. For example time trialing. If on a 40k course I average X watts, then if I know that if I want to go faster I have definitive value that I need to increase. Speed, HR and PRE would not assist in being able to measure accurately the gains made from training (ok I'll spell it out, speed is affected by too many environmental aspects, HR is at its ceiling and lags after effort has increased/decreased and PRE is always the same - totally shagged).
Also, the PM has also allowed me to identify points on a specific TT course where and when I have taken my foot off the pedal (so to speak). This is not reflected in HR data.
No doubt there will be many a rebuttal. Argument for its own sake? Or is there a point to all this?