How did "Bahnhof" become the de facto word to describe spacecraft launch site?

I am not convinced, that the railways-based conotation you seem to claim for Bahnhof actually holds.

A look at the etymology section in e.g. DWDS reveals, that Bahn is a pretty universal term for all types of ways, with Umlaufbahn, Flugbahn as interesting other composite examples.

Gleis, which would today be translated as railways without second thought, originally meant just the tracks as left by cart wheels (see DWDS, etymology section) and so predated railways by some centuries.

Hof is similar flexible term for a single or an ensemble of buildings and the surrounded area, considering Bauernhof, Bauhof, Busbahnhof (no railway required either) or the Hof of a ruler translating to court.

So Bahnhof may boil down to building, where tracks start.

Another possible explanation (use at your own risk)

Die ersten Weltraumbahnhöfe entstanden im Verbund mit Eisenbahn-Anlagen, die für den Transport der schweren Raketenstufen und der Nutzlasten benötigt wurden.

The first space port were built in conjunction with railways that were needed to transport the heavy rocket stages and the payloads.

For example:

Image of Cape Canaveral Space Launch Complex 41, United States

Map (source) of Baikonur Cosmodrome, Russia

This is in fact an interesting observation. I do not have a real explanation, but let me quote from here:

Der Begriff entstand in der deutschen Sprache in Analogie zu einem Bahnhof der Eisenbahn; also ein Bahnhof, an dem regelmäßig Starts stattfinden. Der englische Begriff Space-Port dagegen beschreibt einen Begriff, den Hafen, bei dem eher unregelmäßig Starts erfolgen.

Edited:

The word has definitely been coined before 1970. I found the following advertisement in

Therefore I guess it was introduced by Wernher von Braun. Perhaps you can find more about its origin in the book

Wernher von Braun - Mein Leben für die Raumfahrt (1969, author Bernd Ruland).

Edited:

Two other early occurences of "Weltraumbahnhof" have been found by mtwde and L20:

1. Alle Wunder dieser Welt. Die großen Sehenswürdigkeiten der Welt, von den Pyramiden bis zum Weltraumbahnhof (1968, author Roland Gööck)

2. Der Mensch im Weltall: Die zweite Entwicklungsstufe der Raumflugkörper (1963, author Albert Ducrocq)
   
   Notice the word "Zug" in the screenshot.

Another interesting finding is

3. Armeerundschau, Heft 3/1972, Magazin des Soldaten (1972, Autorenkollektiv) which appeared in the East German "Deutscher Militärverlag Berlin".
   This shows that the word was used in both parts of Germany, and it could even be possible that it is of East German origin, due to the tremendous success of space program of the Soviet Union since 1957. The expression "Weltraumbahnof Baikonur" is a very standard one. The Russian word is "Kosmodrom Baikonur" (Космодром Байконyр) which contains the word "cosmos = Weltraum". Moreover, here you see that

All Baikonur's logistics are based on its own intra-site 1,520 mm (4 ft 11 27⁄32 in) gauge railway network, which is the largest industrial railway on the planet. The railway is used for all stages of launch preparation, and all spacecraft are transported to the launchpads by the special Schnabel cars. Once part of the Soviet Railroad Troops, the Baikonur Railway is now served by a dedicated civilian state company. There are several rail links connecting the Baikonur Railway to the public railway of Kazakhstan and the rest of the world.

This is a good question, because everything else related to space has nautical terms in German to: Astronaut, Raumschiff, Raumfähre

The answer to this probably lies in the German infrastructure. Germany had one of the best railway connections, and if you wanted to get somewhere you would most likely go to the station and travel by train. In most of Germany there are no docks or harbours for public transportation, so the word Bahnhof was simply more related to travel and movement then the word Hafen.