No, the but is appropriate. However, I would remove the comma as well as the article before social. I would also use the plural environments:
Ill fares the land where wealth accumulates but social and natural environments suffer.
This is essentially the same as replacing but with yet:
Ill fares the land where wealth accumulates yet social and natural environments suffer.
As you rightly pointed out in your question, the use of but here is used to contrast two different things, such as in a common expression:
Sticks and stones may break my bones but words will never hurt me.
A shorter version of the sentence in question is simply:
Wealth accumulates but social and natural environments suffer.
If you were to use because, the meaning of the sentence would change dramatically:
Ill fares the land where wealth accumulates because social and natural environments suffer.
Ill fares the land where the suffering of social and natural environments causes an accumulation of wealth.
It's possible that these environments are suffering because wealth isn't being spent on them. It's also possible that wealth is accumulating because it's being hoarded rather than being spent on these environments. (Or maybe both of those things are true at the same time.)
However, while those are possible interpretations about the situation being described, that's not what the but version of the sentence—a simple statement—actually says.
In an analogous example, it's similar to the following proverb:
In the land of the blind, the one-eyed man is king.
The sentence doesn't actually say that the one-eyed man is king because he can see (while the others can't). You can make that assumption—and it may even be true—but modifying the sentence in that way would be to change its meaning in a way that might be false. (Perhaps he became king first and then, through royal research, discovered how to grow himself an eye . . .) In short, all you can know about the situation is exactly what the words in the sentence describe.