The problem with QR codes is that they are read-only.
I don't know about Montreal, but Moscow public transport uses similar paper tickets, also Mifare Ultralight, except you can get them for different number of trips. When you use your ticket, the turnstile or validator would increment those one-way counters so that the next one would know how many trips you have left. You can't do that with a QR code without either the reader or the user's device having a persistent internet connection to some sort of central server that would keep track of all tickets, which is impractical.
I don't know about Montreal, but Moscow public transport uses similar paper tickets, also Mifare Ultralight, except you can get them for different number of trips. When you use your ticket, the turnstile or validator would increment those one-way counters so that the next one would know how many trips you have left. You can't do that with a QR code without either the reader or the user's device having a persistent internet connection to some sort of central server that would keep track of all tickets, which is impractical.