This is indeed how systems around the world do it for NFC tickets. The problem with QR codes is that they're very easy to copy, so the potential for abuse with this approach is much higher. What's to stop people from using the same ticket on two different stations within the sync period?
The QR code can encode (or the system can track, or both) any combination of origin, destination, expiration (or purchase time + validity period), ticket number, etc. Check with the local server that the ID exists with the given information and that the ticket isn't expired, then allow the user through, and the server marks that ticket number as used. If the origin doesn't match the current station, the ticket is expired, or the ticket is used, don't let the user in.
So you would have to buy a ticket every time you go somewhere. That would work for tourists, sure, assuming there are vending machines that can print those QR codes. But it would not work for locals (imagine everyone buying tickets during a rush hour), and even for some tourists, it would be a nuisance. If you're visiting a city and you know you're going to take the subway N times, you would just buy N tickets, but with this system no such thing is possible.
And what about all those transfer discounts some cities have? Like if you're taking the subway and a bus within some timeframe, you still only pay once.
