King Daniel wrote:
The novel DTI: Forgotten History
goes into detail about this, and explains why so few people know of the technique (and even fewer are able to use it) in the Next Generation era.
Of course, the real life reason is that an easily achievable undo button robs any story of consequence or tension, so they just pretended it didn't exist.
There is a unique phenomenon the Enterprise experienced fairly early on - the "cold start" in Naked Time
. As Spock said, it stemmed from a theory on the relationship between time and antimatter.
That would make a lot of sense that the Enterprise engines were already running a unique intermix which allowed them to accidentally time-travel with the slingshot maneuver in "Tomorrow is Yesterday" and no other ships accidentally have done so in the same manner. That way, only certain knowledgeable people like Spock or Scotty could modify the BOP engines to do the same thing while other ships don't have this ability.