I think the only possible answer is the Muggle-borns.
Obviously, the wizarding world has to stay secret from Muggles. But they also must recruit untrained wizards from the Muggle families that birthed them.
Say you're a parent. Your child has always seemed...odd. Different somehow. Special. Interesting things happen around them - often unexplainable, but you rationalize it.
Then they turn 11, and an OWL arrives carrying a parchment letter, sealed with wax, that shatters your world (it could also come by post, of course, which wouldn't change things much). The letter to your child says that magic is real, and your child is a wizard. Your plans for their education go out the window - they have this potential that they must develop.
Most Muggles have never considered magic even potentially real, not since they were children. The thought that there may actually be witches and wizards will frighten you, at some level.
You journey, possibly aided by a mysterious witch or wizard - one of your child's new teachers, to a place you had never imagined could be in London - Diagon Alley. There you see obvious magic, you see potion ingredients that may sicken you, you see, smell, and hear bizarre things.
Perhaps you are calmed and reassured by the teacher. Perhaps Diagon Alley helps you come to terms with things. Perhaps, after all of this, you are actually looking forward to seeing your child grow into a wizard or witch.
Then the Knight Bus shows up, BANG!ing around, careening to and fro with no apparent regard for anyone's safety.
Or maybe a teacher shows up out of nowhere, and makes your child vanish before your eyes.
Or perhaps there's a portkey that they use, and you see your child dragged away by an old boot.
Or they could use a train. A bit old fashioned, it's steam-driven, but you take your child to a perfectly normal train station, enter Platform 9 3/4, and see them board a train that chugs away.
Which way will scare a Muggle parent least?
Also consider the psychological effect on the new Muggle-born student: They leave their parent in a fairly normal way, and their true introduction to the wizarding world is slow - they meet their fellow students, see some minor magics performed. They see interesting and magical treats on the cart. They interact with older students, and the people they'll be spending the next several months living with.
Then, a few hours later, as the sun drops towards the horizon, they get their first view of Hogwarts - a mighty castle, thrusting tall into the darkening sky. Every window blazes with light, and you are awed.
By this point, you are not just ready to learn magic, you are EAGER. Ask any teacher, they'll tell you: the best students are those who are motivated to learn.
TL;DR: It makes the separation easier for Muggle parents and eases the transition of Muggle-borns into the Wizarding world. It also helps drive the students to want to learn, making the teacher's jobs that much easier.