People have mentioned burning and recycling, but I've been toying with an even "greener" approach...composting.
Junk wax era cards, as opposed to some super glossy later cards, are actual cardboard. If they were shredded, they'd work well as the "brown" in a well-mixed cardboard.
Wax boxes would also compost fine. I imagine the wax used in wax packs is petroleum based, as opposed to vegetable based, so they'd be out. I guess those would burn well if someone wanted to have that bonfire still.
I imagine most plastic wax wrappers would be recyclable in places that have plastic bag recycling programs.
In theory, if we could compost junk era cards en masse, we could solve a few problems:
It takes 20,000 pounds of compost to raise the organic matter in 1 acre of land 1%. To get 20,000 pounds of compost, you need about 200,000 lbs of raw organic material to decompose. Increasing soil organic matter makes it better at growing things, hold more water, and sequester carbon so that it's not released into the atmosphere.
Junk wax is near worthless because cards were produced by the millions. To see any substantial increase in value, a good portion of these cards would need to be removed from circulation.
5,000 cards weighs about 25 lbs. So, about 40 million cards per acre should do it.
I think when I build my larger composter this spring, I'll give it a try at a small scale and see how it goes.