Wall of text follows but I hope you find it worth while.
Let me preface by saying that I understand the premise and possible breakage of game mechanics/balance by letting a TAC officer train engineering officers in the top level of ET3, EPtW3, DEM, etc... It would also diminish the variety of starting race traits and professions by essentially allowing the player to shoot for a specific captain power (ex APA) while maxing out the BO's for the specific ship synergy of his choice. There should be an alternative that does allow some flexibility however.
I propose the following 2 options:
Train Rank 1 Abilities: I'm an engineering captain extremely proficient in starship battle strategy (LVL9) . I groom and teach subordinates based on this vast experience. Although I may not be able to teach the finer points of a specific skill set, I understand the principles of employing Attack Pattern Omega (Rank 1) in an effort to save the ship and should be able to teach bridge officers the concept.
Letting each captain teach basic skill sets to his subordinates would give the player a feeling of connection with his crew and every game excursion an episodic feel. Say for instance you enter a system with an unknown entity that wants to destroy you. Their weapons are completely dismantling your shields and 8 legged beings are boarding your ship! You're a scientist in a non-combat vessel, on a peaceful scientific mission! This shouldn't be happening, but you must save the crew. Quick, you have an idea... If you can reverse the shield polarity (RSP 1), it just might give the insectoids pause and time enough for you to mask your energy signature and escape via evasive maneuvers (or configure a spacial anomaly, drop his shields, and add some high yield torpedo's to his diet)!
Letting the properly specialized captain train rank 1 of any abilities he has maxed does not break the game, it still costs the same amount of merits as going to a trainer, and it gives him some flexibility in his long missions away from home (or star bases) for years at a time.
Captains Train Profession Specific Rank 1, 2, & 3 Abilities: This just seems to make good sense. If you're an engineering captain and able to train Engineering Team 3, it makes common sense that you would be able to teach the line of progression (ET 1&2). Just because an engineering captain is tasked with captaining a defiant, shouldn't mean he has to return to space dock to find or train able bodied crew that he should already have!
"I'm sorry Scotty, we just lost Ensign Davis during our last mission on the Insectoid front. I know he was your favorite trainee and led ET 1 but we've got some hard choices to make. You're a miracle worker and the best engineering team leader I've ever seen (ET3). Your skill in manipulating the structural integrity field is 2nd to none (APtSIF 3). We've grown together as engineers and I've had you with me through all my commands but, I can't use you on this ship. Further more, I cannot teach you anything about this ship (ET2) and you cannot learn without heading back to the academy for officer training (ET1). Even though I am a fully qualified technician (LVL 9), there is no other choice. Please go back to your quarters now and contemplate ways you can repair our hull damage with emergency power in weapons or by diverting power from the shield extension system you've come up with."
This isn't a change in game mechanics or balance. It allows players to spend the vast amount of merits and BO skill points they've acquired on the fly to make their officers and ship more flexible in the areas they specialize. Any feedback or criticism is welcome!