When Writers Are Historically Illiterate

First, let's look at this scene from Star Trek; The Next Generation, "I, Borg" from Season 5.

Ok, so that's the episode I'm referring to. Unfortunately, it's hard to find the exact clip on YouTube. But basically, they're thinking about their newly discovered option to kill the entire Borg Collective.

LAFORGE: If this works the way I think it will, once the
  invasive programme starts spreading, it'll only be a matter
  of months before the Borg suffer total systems failure.
PICARD: Comments.
CRUSHER: A question. What exactly is total systems failure?
DATA: The Borg are extremely computer dependent. A systems
  failure will destroy them.
CRUSHER: I just think we should be plain about that. We're
  talking about annihilating an entire race.
PICARD: Which under most circumstances would be unconscionable.
  But as I see it, the Borg leave us with little choice.
RIKER: I agree. We're at war.
CRUSHER: There's been no formal declaration of war.
TROI: Not from us, but certainly from them. They've attacked
  us in every encounter.
PICARD: They've declared war on our way of life. We are to
  be assimilated.
CRUSHER: But even in war there are rules. You don't kill
  civilians indiscriminately.
RIKER: There are no civilians among the Borg.
PICARD: Think of them as a single, collective being. There's no
  one Borg who is more an individual than your arm or your leg.
CRUSHER: How convenient.
PICARD: Your point, Doctor?
CRUSHER: When I look at my patient, I don't see a collective
  consciousness. I don't see a hive. I see a living, breathing
  boy who's been hurt and who needs our help. And we're talking
  about sending him back to his people as an instrument of
  destruction.
PICARD: It comes down to this. We're faced with an enemy who are
  determined to destroy us, and we have no hope of negotiating a
  peace. Unless that changes, we are justified in doing anything
  we can to survive.
SECURITY [OC]: Security to Captain.
PICARD: Picard here.
SECURITY [OC]: The Borg has regained consciousness, sir.
PICARD: Acknowledged. We proceed with the plan.

What Crusher says makes me cringe, "There's been no formal declaration of war." She further supports this with the line, "But even in war there are rules. You don't kill civilians indiscriminately."

From the writer's room, in their own context at the time, I'm sure this all made sense as a sensible rebuttal by Crusher. But it's not. It's stupid thing to support your overarching point with. The overarching point Crusher was making had more to do with genocide and how that aligns with Starfleet and Federation values might be valid. But she was written to support this possibly valid point with a weird artifact of 19th century colonialism.

But surely by the 24th century, senior members of a starship exploring the galaxy must realize what it meant to have a "formal declaration of war" and how that would be completely different from a planetary population in the 20th century writing a sci-fi story.

This is what makes her lines so jarring. In order to have a formal declaration of war, you have to have some kind of channel to express the declaration. This was only the third documented encounter with the Borg. There were no channels between the Federation and a pan-galactic race of cybernetic life forms they just recently encountered three years before.

It's not like hostile races all have a rule book that says, "When you encounter Humans, before you fire on them, make sure you say 'One, Two, Three, Four! I Declare A Space War!'"

A more realistic exchange where Crusher still says something stupid but the rest of the crew isn't stuck in a 20th century writer's room:

CRUSHER: There's been no formal declaration of war.
TROI: Are you feeling alright, Beverly?
DATA: Doctor, the Borg have not petitioned the Federation for
  diplomatic relations at any time.  There is no credible
  precedence for an unrecognized military organization to declare
  war.  Even if there was, it would not justify their attack
  three years ago at Wolf 359.