In past eras they used holograms and watermarks and special papers in an attempt to prevent forgery but these methods keep getting challenged by an ever more sophisticated criminal element. Moving into cryptographically secure methods is the last barrier here.
They could also rely on the state to match identities to tickets, but this approach does not scale and is frankly undesirable for the majority of people anyway.
The "problem" they were trying to "solve" is letting people sell some of their tickets to third parties, but not all of them. That is understandably how they arrived at a mobile application as a solution
But the problem of admitting the original ticket holder is simple as shit. Just .... check his ID?
Even if we could make them truly unforgeable, people generally want electronically transferrable tickets. How do you propose to do this?
Don't bother your season ticket holders about getting their own person admitted! I am standing in front of you, bearing identification, and you are whining about a mobile app?
They could even do something like give him a little RFID token that can be used once. Tap it, gates open, go in, done.