Baseball is a business, trainers etc, are part of that business.
Should we all learn to take care of ourselves better and become less reliant on doctors and drugs? Absolutely! Is their obvious vested financial interest in the continuation of the healing over prevention medical model- you bet!
The greatest advantage of trainers is their advantage to technology, although becoming wholly dependent on that technology engenders a whole new set of problems- its a delicate balance. The necessity of having expanisive coaches and trainers is related to two big factors you didn't mention.
One is that players are not really self-dependent. They are pampered at an early age and, relish the codeling and attention and don't develop self-reliance to much later than they would otherwise. The other is the importance of following orthodoxy in the era of intense media scrutiny. Trainers and coachers are part of the baseball establishment any organization. Backlash for renouncing trainers would be huge, creating a media field day. The stigma against being self-educated feeds adds to the (somewhat contrived) need for pseudo-authorities/gurus. The players are not in need of the trainers so much as they are dependent on them.
Overall, trainers and coaches provide help, but the extent to which they allow players to achieve, beyond what they would by applying "themselves" is not as drastic as some may think, IMO. There have been numerous accounts of coaches ruining pitchers' careers too.
The references to the character of the players, and even to race- were a related to your hypothetical '05 Yanks vs. '27 Yanks match-up to point out the sheer skill level of the players was only one component, and not the totality of the equation.