Many western European languages use words related to port or base to describe rocket launch complex.
I found it interesting, that only in German language (out of the ones I have been able to look at) Weltraumbahnhof seems to be more commonplace word to describe such place, than Weltraumhafen which had naturally come to mind in similar fashion to Flughafen.
Though Raumhafen may have become more popular in books according to NGram Viewer, news reports of launches still seem to predominantly use Weltraumbahnhof.
Was there any reason behind this adoption?
It seems that the concept of a "Space Station", which is now usually called Raumstation was often referred to synonymously as Weltraumbahnhof back in early 1960s. I found a Spiegel article from 1962 (Amazing I can do a full text search for free from so long time ago!!!) with the following quote:
Tatsächlich hatten diese Raumfahrt -Pioniere schon vor Jahrzehnten Weltraumstationen ersonnen, die als Startplatz für Raumflüge in das Planetensystem gedacht waren. Zu einer Zeit, da noch keine Weltraum-Rakete gebaut worden und keineswegs gewiß war, daß jemals eine gebaut werden würde, mußten diese Weltraumbahnhöfe utopisch anmuten.
A book written in 1963 was also referring to space station as Weltraumstation.
Interestingly enough, another article from Spiegel 5 years later (1967) has the following quote:
Zum US-Weltraumbahnhof Cape Kennedy brachte er Farbaufnahmen zurück, die den Wissenschaftlern zeigten, wie flach die Gashülle der Erdatmosphäre ist.
In comment and answer, mtwde and Paul Frost posted examples of Weltraumbahnhof written in respectively 1968 and 1970 referring to a grounded complex. So something might have happened in the decade to change the terminology. I've found another example from a book in 1971.