Doesn't this seem extremely unnecessary? Hedwig is an Wizarding Owl, she can fly and can travel wherever needed with minimal instruction. Hedwig in particular is very loyal and intelligent. There are more than a few examples where Hedwig isn't confined to a cage while Harry travels and there is no problem. They let her out to fly in CoS when The Weasley brothers rescue Harry with the flying car. She finds Harry in The Leaky Cauldron in PoA without any instruction, she even found her way into the Black house while it was under a Fidelius Charm. She will find her way to her needed destination without being bodily packaged and trundled there.
Of course it's not just Harry, all students seem to force their owls into cages in order to travel with them. Apparently for no good reason.
One proffered reason for Hogwarts students needing to do this would be because of the protections from outside interference that are placed on the school, but I'd argue that's nonsense. Wizarding owls flock to Hogwarts every morning, and sometimes at other times, to deliver mail. They seem to be one of the few creatures with almost uninhibited access to Hogwarts (except for them being searched regularly in OotP).
The movies usually make poor changes to the story in order to fit things into a film script, but occasionally they change something for the better. It's one of the great changes in the Harry Potter movies when Hedwig-
gets to sacrifice herself to protect Harry instead of the extremely undignified and helpless end in the book.