Actually, that is precisely what you are suggesting, that the Sabbath is about resting because man tends to "overwork." Actually, God provided another remedy for weary, overworked men and women, and it's not His Holy Sabbath, it's sleep.
The point is that God Himself "rested" on the 7th day and hallowed it so the purpose of the Sabbath is not simply to "rest" in the sense you are using, to rest so as not to overwork oneself. The reason God rested wasn't so He wouldn't overwork and become ineffective, it was because His work was finished. And that's what the Sabbath means, to rest from works not to avoid overworking, but because the works are finished.
So again, the New Covenant is about a day when God's people would enter into rest with Jesus, not because we are tired or overworked, but because the work of reconciling us with God is finished. "It is finished." (Jesus' last works on the cross) You can rest in faith that you are now acceptable to God through the blood of Christ which, though our sins be as scarlet, they are now washed in the blood of the Lamb and are white as snow. And that's the Gospel truth.
In Christ,
Pilgrimer