EVERYONE PLEASE READ
The "paper" tickets are used because that is all that is available to print on if you get your tickets / annual pass from any Disney park (as well as TTC, Guest Relations, and Downtown Disney). The printers are loaded with a reel of the tickets, they are not individual pieces of paper that they can switch out. Since any given Disney ticket venue has to sell anything from 1 day tickets to Annual passes they have to have ticket system that is consistent. If they were to have a different printing area for regular tickets and a seperate printing set-up for Seasonal or Annual passes it would be time consuming for the Guest and Cast Member, and it would not be cost effective either.
The plastic tickets that you may see are from Disney Stores, Disney Resorts, or tickets that were ordered online and sent to the Guest's home.
I hope I explained that well. And again if you keep your ticket in a sleeve they generally will last a good while.