My non-native guess is that using av would imply that the map is literally made of Sweden, as if it were a substance.
No, "karta Sverige" sounds rather weird to me, and I'm a native speaker. I think it may be because "kaffe" is a substance, and "Sverige" is more a conceptual thing. "En spann jord" (a bucket of dirt/earth) also works, but not "en karta Jord" (a map of Earth) I'm not sure though, I'm very bad at actually knowing the grammar of my own language...
(A bit late to the party, I know) Both are somewhat ambiguous to my ears. Sveriges karta sounds to me as though the map is owned by Sweden. Imagine a very old and famous map owned by the Swedish government, if such a thing exists. Den svenska kartan, on the other hand, could also mean that the map was made by Swedes or in Sweden. I'm only a learner though, so if any natives don't agree with me, feel free to correct me.
Do the historic semantics of this sentence equate to a map 'over' Sweden, as in a bird's eye view map?
This would make a better experience for uaers at the highest language skills, who could save typing time to insost in the vocabulary and grammar that we never get right. Duolingo is great for begginers, and in this way it would also be great for users on intermediate or advanced levels