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.
So the central server model is practical. The user's device has to have an internet connection at some point to activate the ticket within a reasonable period before using it but the connection doesn't have to persist after that. I don't know how their handheld scanners work in the Hudson River tunnels where there is no cell service but they do, so long as the user activates their ticket before the train departs.
https://news.social-protocols.org/stats?id=41791369
https://news.social-protocols.org/stats?id=41815614
https://news.social-protocols.org/stats?id=41821336
Note the orange line indicating rank, which in every case shows a very sudden and precipitous drop in the rank of each post.