It is well known that Hogwarts' students have to get through a barrier between Muggle Platforms Nine and Ten in order to reach the magically concealed train Platform 9 3/4 at King's Cross Station and gain access to the Hogwarts Express.
I have detailed all Harry Potter movies, and I haven't seen anyone crossing the wall without the clanky luggage trolley.
It is understandable for freshmen to use the luggage trolley as they face the apparent brick wall since clinging to the handles and leaning low behind the bulky trolley provides confidence and a form of protection in case something goes wrong. One may also argue that trolleys are useful when carrying heavy trunks and cages, as Hogwarts students do, and that they serve to mask the casual vanishing act from Muggle eyes by looking like you are simply wheeling the trolley with your luggage along.
Perhaps I'm answering my own question with my conjectures, but I wonder if there is a canonical answer about the trolleys being absolutely necessary or not to get through Platform 9 3/4 in order to reach the Hogwarts Express, at least -of course-, if Dobby doesn't block the magical barrier.