An aside -- pherank's comment above, that Astaire "liked to do his own choreography" got me curious about that process, so I did a tiny bit of digging. According to IMDB, Astaire danced in about 30 films, but got screen credit for some kind of staging or choreography for 5 of them (and did some kind of "uncredited" choreography or staging for another four) Hermes Pan (who doesn't get nearly enough recognition for his work) was credited in one fashion or another for 14 of those films, and mentioned for uncredited work several times as well. Eugene Loring gets credited four times; and Robert Alton and Alex Romero get three credits.
Astaire must have been responsible for the bulk of his personal material -- it has a stylistic consistency over the span of his film work that would be very hard to imagine if he were dancing numbers totally created by a number of other people. But it's fascinating to realize that, as far as film credits are concerned, he was only minimally involved in creating the sequences he danced.
What you say about Astaire not receiving mention for choreography was often true, but there are countless instances of cast members and dance partners saying, "but Fred put together all that…" And in his Broadway days, Astaire devised countless routines. Under Hollywood's star system, project assignments (and thus credits) were assigned before a project had even begun, so we do see some situations where credits go to persons who had next to nothing to do with a project. Hollywood was (and is) all about power politics, and who you know. Not so much a meritocracy.
Absolutely recommended reading: The Astaires: Fred & Adele (look for it on Amazon.com using the Ballet Alert Amazon Search). You'll learn all about the 'fabulous' Adele Astaire who was perhaps the most recognized star of her generation - now mostly forgotten due to the lack of film evidence of her work. She's been reduced to a rumor. There are very interesting parallels between the Astaire parents (especially Mom) and Suzanne Farrell's parents and numerous other "stage parents" you may have read about. I see a pattern forming...
[Edit] I just ran across this page on Wiki that attempts to list all of Astaire's solo and partner FILM dances, and there's this interesting quote:
Astaire nearly always collaborated with other choreographers, and except for the choreography of choruses which Astaire avoided, it is generally not possible to determine with any certainty the extent of Astaire's contribution vs that of his collaborators. This is particularly true in the case of his principal collaborator, Hermes Pan, where the seamless nature of the collaboration has been described by Astaire's rehearsal pianist Hal Borne, the only independent witness present throughout the entire process of dance creation of the Astaire-Rogers films: "It was hard to figure who contributed what to the choreography". Borne also describes the working atmosphere of such collaborations: "It was always pleasant. Never a hint of unpleasantness."
So I may have to concede on this point: Astaire worked with Hermes Pan mainly on his film musical projects. And that explains also why Astaire is able to keep "stylistic consistency" throughout these projects. The Broadway work of the Astaires was a different matter though.