Paper tickets, yes. Paper boarding passes, no. Replacing a paper boarding pass has been easy since airlines switched to an electronic ticketing system where the actual ticket is an entry in the airline's database.
The person I was responding to was talking about tickets. I will print a paper boarding pass if I'm at home and I can print it easily when I check in in advance but I just do it at the airport if it's not convenient. (I don't like making myself more dependent on my phone than I need to be.)
That comment introduces some confusion with "moving travelers from paper tickets to the use of their phones" before giving a mixed list of benefits of e-tickets and mobile boarding passes.
E-tickets were introduced in the 1990s, and essentially all airlines were using them by 2008. They don't have anything to do with phones. Mobile boarding passes are a more recent development.