There are at least two advantages of always keeping your boarding pass after arrival.
For one, if after you exit the plane, you suddenly realise a coat or a small bag was left behind...for security reasons you will NOT be allowed to go back into the aircraft and pick up that item you left behind. if you have your boarding pass however, there will be an airline staff person who you can ask for help. They will contact the cabin staff, give them your seat number and what item to look for, and often someone will arrive in a few minutes with that item for you.
Secondly, even after you leave the airport, if for some reason you lose your return ticket...the local airline office can use that boarding pass to access your flight info from the airline computer system....and thus verify that you did indeed purchase a return ticket. They may charge you a fee to re-issue that ticket...but that's better than having to buy a new return ticket.













