It’s easy to predict how the Federation will react in any situation involving the Prime Directive: They’ll always take the course of action that violates it to the maximum degree possible. And then the captain involved will probably get a promotion for it.
And how did I not know that Zefram Cochrane launched his ship from Bozeman? There are enough nerds there (it’s a college town) that you’d think there would be some sort of commemoration of that.
Admittedly, this is my take too. But for political-military reasons, I can see the point of @RickJay in his post.
My problem with this is that IIRC, Cochrane launches from a silo. Unless Cochrane went to some great expense after WWIII, there aren’t any silos near Bozeman.
But, I haven’t seen First Contact in awhile.
Tripler
Hell, I’ve got a lot of re-watching to do . . .
There are still another 40-some years to put the silos in.
It may already be there if you consider that Star Trek history diverged form ours in the sixties.
I know, filming locations can be anywhere, but that silo was in southern Arizona. You can visit it.
It has the benefit of looking like what an average person thinks a missile silo looks like, because it was built in the 60s. Originally, it probably had consoles with lights that flashed out of sequence, too, and huge tape drives spinning back and forth. 
The Temporal Police keep removing it to maintain the timeline. Can’t let the contemporaries know their future.
Just dropping in to say that I noticed what you did here.
I wonder if that’s how some humans feel about whatever race Carol Kane belongs to in Strange New Worlds. And Whoopi Goldberg’s too, while we’re at it. Thanks for living among us and not helping out, guys. Were a few hints about penicillin or not digging the outhouse too close to the well too much to ask for? “It’s our policy to let you suffer. We just watch” doesn’t sound enlightened to me.
We’ve been working our way through the better Star Trek movies, and we just finished First Contact.
I can technobabble away the OP’s problem, as in 1986 the Vulcan’s didn’t have the technology to detect warp signatures at the range necessary to find the one’s from the Bounty.
My biggest issue with First Contact is the original coincidence that Cochrane’s ship hit warp just when the Vulcans were passing through, and close enough to detect it.
I liked my wife’s explanation quite a bit. The Vulcans were in the solar system to investigate the temporal anomaly or chroniton particles or whatever created by the Borg’s time hole. A phenomenon they could detect from some distance away.
By the time they arrive the Borg sphere has been destroyed, and the Enterprise is running quietly due to the internal battles. So the Vulcans either don’t see anything, or they do see the Enterprise or Borg, which clearly aren’t from 2063 Earth, and decide to leave.
The Vulcans drop in, do some scans, and are getting ready to leave, when the Phoenix goes to warp, which then leads to first contact.
This nicely converts the initial coincidence to a time paradox. A galaxy saving coincidence is lazy writing. A time paradox is a well honored tradition in the Trek universe.
…and ALSO lazy writing.
That’s a dandy fanwank. Well done, Mrs. echoreply!
Seconded!
Side note: someone mentioned chronitrons and baryons at work yesterday, and I realized they were pulling my leg due to Star Trek Day.
Tripler
I worry about the fission products of chronitrons.
Just reverse the polarity. It’ll be fine.
Magnetic polarity. Please.
Reverse the magnetic polarity on what? It’s gotta be the anti-tachyon generator or something.
On the photon torpedo shooter-outer.
As long as the “outie” part doesn’t become an “innie” part the torpedo-shooter oughta be good.
Reverse magnetic polarity chronitron torpedoes? They didn’t cover those in EOD school. . .
Tripler
I graduated in '09, probably a couple hundred years too early.
On the deflector dish, which is really just a giant Sonic Screwdriver installed on the front of every Starfleet ship.
When they ran into her, she seemed particularly ignorant of anything technical. I don’t know that she had any particular expertise to give anyone. (She didn’t acquire engineering skills until much later in life, apparently.)
It’s sort of like if the average person got sent back in time to the middle ages. They’d have some vague ideas about the important of hygiene and stuff, but they wouldn’t have anywhere near the knowledge to become some kind of genius inventor that can push humanity’s technology forward. There’s a massive difference between knowing things can exist and knowing how to actually make them happen.