There is actually another mention of the train tickets in the books, though in a sense it's actually an earlier mention. In Half-Blood Prince When Dumbledore takes Harry into his memory of the first time he met Tom Riddle, the train ticket makes an appearance:
"All the details are on the second piece of parchment in your
envelope," said Dumbledore. "You will leave from King's Cross Station
on the first of September. There is a train ticket in there too."
So 50+ years prior to Harry, Tom Riddle received a train ticket as well.
However, there is no mention of the tickets ever being checked or collected. Furthermore, the only two mentions of the tickets are both for new students, and not just any new students — specifically new students with no knowledge of the Wizarding world.
It is thus possible that the tickets are not really meant for allowing entry onto the train. They may simply exist to provide information, especially to students who would be otherwise unaware. As Hagrid mentioned in the quote you cited in the question, the ticket contains the information about where the student will catch the train. While most people will know that the train leaves from Platform Nine and Three Quarters at Kings Cross at 11:00 on September 1st, it is useful for those students like Harry and Tom Riddle who would not otherwise have that information readily available to them.
Since the series follows Harry's point of view, there is no reason to expect to hear about the tickets again since after his first year he know longer needs it as a reference aide.
On the other hand, according to JK Rowling on Pottermore, there was a Squib who snuck into Hogwarts:
On the appointed day, his big brother Hamish took him to Hogwarts on
the back of his broomstick, hoping against desperate hope that Angus
would be allowed to stay once they got there, or that the school might
be able to tease some magic out of him.
It is perhaps notable that he did not simply take the train. Perhaps this is because he did not have a ticket, which would then indicate that tickets are actually necessary. However, it is also possible that they simply didn't want to risk being caught on the train and sent back before getting to Hogwarts. Moreover, this took place in the mid-nineteenth century, so the rules might have been totally different at that time, for all we know.
Additionally, it kind of makes sense that tickets wouldn't really be necessary for getting on the train. No one is paying for the train ride so there's no problem of people sneaking on without paying. And (for the most part) anyone who is not meant to be on the train wouldn't be able to get on with or without a ticket.