Problem with that is the Vulcans were right around the corner. Seeing a highly advanced starship tractoring in this little vessel to this primitive world may have aroused a lot of suspicion. They were trying to stay hidden from the survey team, remember.
However, they did come back during the day, as I recall, and the Vulcans arrived at night, so there was a period of at least a few hours between the time the Phoenix returned from her run and the Vulcans arrived. Should be plenty of time to get the ship down, especially with shield extensions or some such.
I did think that a possible concern with leaving the warp engine section in orbit was it perhaps being a bit of a prize in what would probably be a politically unstable post-WWIII period, assuming several nations or corporate entities still had access to LEO. The TNG pilot did suggest things were still pretty rough, at least in some places, even by 2079.
Agreed. I am not sure Cochrane would want to leave it up there, especially since he himself likely didn't have access to another launch vehicle that would get him to LEO to recover it, but would be at the mercy of some other party.
Now, having invented it, he'd still be very important since anyone who could get up and recover it would not know how it worked and would likely not want to take the risk of permanently damaging it while trying to reverse-engineer it. So he certainly had some cards to play that could influence him to just bring back the nose capsule...
It *would* be useful to leave part of it in orbit. Easier to get back up there if you don't have to carry so much mass. But how easy would it be to reattach the warp drive on an EVA?
Perhaps he just left it at the ISS or its successor. Assuming a post-nuclear world would have the resources to maintain a space station of any kind....
It appears that at least North America and Western Europe (along with Japan) weathered World War III very well, considering how many of their major population centers appear in the 24th century much as they did in the 21st. San Francisco, for the most part, is unchanged. Same with Paris. And Washington D.C. evidently made it through okay if the Smithsonian is still around, even if the Phoenix is actually in an orbital annex and not over at Udvar-Hazy in IAD.
And within just a year or so of First Contact, the
Valiant was heading out to the Galactic Rim, so there must still be extensive and robust aerospace manufacturing facilities around.