Why crows? Are they noteworthy for flying in straight lines?
Why not, say, carrier pigeons, which are famous for that?
(It reminds me a little of Charles Dickens’ musing on “dead as a doornail”:
“As the hawk flies” would be a funny twist on the phrase, since hawks are famous for gliding in slow lazy circles and not really going anywhere until they dive-bomb a vole.
Or perhaps “as the penguin flies”. I don't know what that should mean but it can't be good.