Global forever stamps are $1.20 at retail, so that's the upper bound on their postage expense and covers all UPU countries[1] (incl DPRK, Syria, Russia, etc). Antartica actually only requires domestic postcard rates ($0.34) as it has a domestic zip code (96598).
An an American living in Siberia, I can say that Siberia is pretty civilized. The government mail is pretty reliable for things that don't look "interesting". [1] I've personally received postcards from the USA without a problem. It's certainly not comparable to North Korea or Syria.
[1] The Russian post has a reputation for stealing foreign mail that looks like it might contain money, information about money, or credit cards. I haven't tried it myself: for important stuff I use FedEx or DHL.
I'd imagine they use the profit from domestic shipments to help subsidize more costly international ones, if it's really $3 regardless of destination.