Why is it "could" and not "can" in the famous line: "If a face could launch a thousand ships"?

To start with, could can be read as a conditional. It could launch a thousand ships if the conditions are right.

Secondly, you can indeed read it as past, because it refers to a (mythological) past event.

It is a reference to the quite famous story of the Trojan War. That war, as legend has it, was waged because the prince of Troy abducted the most beautiful woman in the world (Helen).

Because of that, the Greeks assembled the biggest assembled fleet they could, rumoured to be a thousand ships, to besiege Troy. This is all very nicely described by Homer, a Greek writer.

Helen was said to be so beautiful, that her face launched a thousand ships.

Jim just to be clear,

the reason that in that song it uses "If a face could launch a thousand ships"

is because that phrase is a pre-existing well-known phrase.

(The whole point of the song, is that the sonf is an "extension" of that well-known phrase .. does that make sense?)

In answer to your other question, why -- in the original phrase -- do we tend to say "could" rather than "can" .... I have absolutely no idea.

It might be there is "no reason" and you are completely correct: either it would be better to use "can" or "can"/"could" are absolutely equally justified by the English grammar board.