Trahan plays at a high level, so what he says must be right. That's just plain bad reasoning for the same reason your Nicklaus example ( he used thoughts and he did okay) is faulty logic. What Trahan says is IN FACT wrong:
"To swing a club you have to have thoughts, as swinging a club is not an automatic system built into the body as is breathing and balance"
First, it is incorrect to say you HAVE TO HAVE THOUGHTS to swing a golf club. In the context he is saying you have to have swing thoughts, and this is absolutely false. I have thoughts when I swing a golf club, but they have nothing to do in any fashion with golf, here are some of my thoughts when I swing.
Trust in the Lord with all your might lean not on your understanding
I like pizza and pitas too and everything in between
Mary had a little lamb I wish I had one too.
Singing Sweet Home Alabama all summer long
To play a shot, I first think in detail about the shot and what I want to accomplish, as Trahan does during pre-shot, Trahan and others call this visualization - I ABSOLUTELY AGREE THIS TO BE AN ESSENTIAL PART OF PLAYING A GOOD SHOT. But once it is "go time" as I begin to step around to the ball ....all conscious thought about the swing, it's outcome, how to make it, etc. are turned off. Instead I occupy my mind with thoughts TOTALLY UNRELATED TO THE GOLF SWING as above. I DON'T need swing thoughts to swing a club.
Secondly, though the golf swing is not "like breathing", it CAN BE BUILT INTO THE SYSTEM as a learned motor activity that functions at a level that is beyond conscious direction - like other learned motor activities we do without thinking about - riding a bike, driving a car, typing on keyboard, skiing, brushing our teeth...the list is endless. Bertholy and Clearkey have been asserting this for several decades. Bertholy saying the swing must become a "conditioned response", and Clearkey taking it a step further by declaring that conditioned responses deliver their best results in execution when there is a deliberate attempt to disengage the conscious mind from the execution of the swing.
The science (outside of golf) behind all this is not new, but is ongoing, and increasingly well documented. In one fascinating study, two individuals who had lost virtually all capacity for declarative memory and conscious learning due to temporal lobe damage caused by herpes were given a specific motor task to perform. From the study:
"The volunteers were presented with the same series of 8 pairs of miscellaneous objects and asked to select the correct one of each pair, in several sessions conducted over several weeks. The word correct was on the bottom of the correct object, and could be read after the object was picked up and turned over.
At the beginning of each session, the volunteers had no recollection of having performed the task previously, and even after several sessions they could not explain what they were being asked to do or why. But, after several sessions of repeating the exercise with the same pairs of objects, the volunteers unconsciously selected the correct item in each pair with increasing accuracy.
The ability to select the correct object appeared to be automatic. In fact, during the course of the study as they were able to select the correct object, the subjects wondered aloud, How am I doing this?. When asked how he knew which object to select, one of the subjects pointed to his head and replied It's here, and somehow or another the hand goes for it. By the end of the study they were scoring 95%; and 100%; in their selection of the correct item.
So to use your example of Jack Nicklaus - who you say he uses swing thoughts and "did okay" - if he lost his capacity for conscious memory, becoming perhaps even an amnesiac, he could still hit a golf ball without swing thoughts ( because he couldn't access them or even remember them). He would be the Jason Bourne of Golf!
And to take it a step further, studies outside of golf have demonstrated that stressors to our system - anxiety for example, have a direct negative impact on that area of the brain where habitual learned motor activities are stored and controlled. Even more to the point of what we are talking about - Once a stored activity has begun to send the signals for execution, input from sources outside will cause a misfiring of the impulses and the execution will be severely diminished - you get the yips...or the yanks...or the duffs.
For someone like me, it is hard to wade through all the science and neurology terms like striatum, basal ganglia, cortico-basal ganglia loops, thalamic connections, etc....but it's all there, and it is all facts. I have no need, and just prefer the "laymans version" as it pertains to golf - Bertholy combined with Clearkey, then you can "build a swing that you never forget", and play golf without using the restrictive bonds of swing thoughts!