Modern shotgun scabbards offer shooters the ability to stow extra ammo, change size, and even alternate carry methods. Modern materials also allow for a greater element of customization and modernization. These materials are even more affordable and easier to manufacture. These materials are water resistant, tear resistant, and resist outside elements much better than leather. Shotgun scabbards these days are made from nylon and cordura materials.
Leather also has a number of downsides and there is a reason its been replaced by more modern materials. Leather is cool and has a flair to it that polymer and synthetic materials never will.