No it is not at the discretion of the airline. As a PR you need a PR card or a PRTD. Yes, eTA is not an option but that is intentional.
Believe me and all the others: You have no chance, literally zero chance, to board the plane without either an eTA or a valid PR card or a valid PRTD. You will make it all the way to the gate and when they swipe your passport there will be a large "Do not board" message appearing on their screen that they will not miss, as previous posters already pointed out. They will then ask you if you have a PR card or PRTD which you don't and they will then deny you boarding. Guaranteed. There is no hoping. Period.
I tried it myself by intentionally not showing my PR card when taking flights to Canada. I tried it with flights from the US to Canada, with flights from Europe to Canada, with flights on Air Canada, with flights on British Airways, with flights on Lufthansa, with direct flights, with connecting flights via a third country... In all cases I made it at most to the gate (if even) and then I was not let on board until I produced my PR card.
So, please believe me and all the previous posters: If you don't have an eTA, a PR card or a PRTD you will not board that plane.