In Star Trek, why do Federation / Starfleet ships always seem to delay returning fire until it's almost too late?

I keep seeing this situation in Star Trek series:

"Captain, they've raised shields!"
"Now they're charging their weapons!"
"Captain, they're targeting our engines!"
"OK Ensign, evasive maneuvers."
BOOM
"Shields are holding, Captain, we're at 25%."
"They're coming about for another pass!"
BOOM

"Captain that one took out our warp drive, shields are offline as are phasers"
"Ensign, target their weapons array with a photon torpedo."
"Captain, they're hailing us..."
"Ok, belay that, put 'em on-screen."

& from this point they're possibly boarded, taken hostage, all kinds of bad outcomes that they have to come back from. One might imagine that a well-equipped cruiser would drill for such eventualities. I'd imagine it more like:

"Captain, they're raising shields!"
"Folks, you know what to do - defend the ship!"
All over the ship the crew work together as a well-oiled machine. Shields go up, phasers take out the bad guys' weapons & engines faster than the other guys can react, while simultaneously the helmsman takes them through a series of seemingly random maneuvers designed to make them a very slippery target.

"OK hail them, see why they made an aggressive move on us."

Any reason why it's always the former & never the latter case?

Answer

It is because of the policies of the United Federation of Planets. The TNG Technical Manual has this to say on the matter, (For those following at home: Section 11.6, 'Tactical Policies').

Starfleet draws proudly on the traditions of the navies of many worlds, most notably those of Earth. We honor our distinguised forebears in many ceremonial aspects of our service, yet there is a fundamental difference between Starfleet and those ancient military organizations. Those sailors of old saw themselves as warriors. It is undeniable true that prepairedness of battle is an important part of our mission, but we of Starfleet see ourselves foremost as explorers and diplomats. This may seem a tenuous distinction, yet it has a dramatic influence on the way we deal with potential conflicts. When the soldiers of old pursued peace, the very nature of their organizations emphasized the option of using force when conflicts became difficult. That option had an inexorable way of becoming a self-fulfilling prophecy.

Today, peace is no easier than it was in ages past. Conflicts are real, and tensions can escalate at a moment's notice between adversaries who command awesome de- structive forces. Yet we have finally learned a bitter lesson from our past: When we regard force as a primary option, that option will be exercised. Starfleet's charter, framed some two centuries ago after the brutal Romulan Wars, is based on a solemn commitment that force is not to be regarded as an option in interstellar relations unless all other options have been exhausted

(bolding mine, italics are verbatim)

Further down the page it says:

A starship is regarded as an instrument of policy for the United Federation of Planets and its member nations. As such, its officers and crew are expected to exhaust every option before resorting to the use of force in conflict resolution. More important, Federation policy requires constant vigilance to anticipate potential conflicts and to take steps to avert them long before the escalate into armed conflict.

Later on (I'm not going to type the full quote because my fingers hurt from typing all of that!) they state that "there are situations in which a starship and her crew can be considered expendable". So the Federation places a very high price on peace /over/ immediate loss of life. Logically speaking going to war causes more loss of life in the long run, so if you take the aphorism "The lives of the many outweight the lives of the few", then it is also a rather logical choice.

So the crew are just adhereing to policy meant to preserve the peace (And I have no doubt that Picard would have valued and cherished these policies very highly).