I think that the Sabbath day is a day where people were in a sense forced to pay God some attention.
After all, you can't work at all, so what else is there to do? Think. Pray. Relate to others. Study the scriptures, etc.
So I might guess that most people would neglect much of that if they did not have one day specifically devoted to God....much like today. Practically nobody observes the sabbath anymore.
The irony is that in past times, religious leaders turned what was supposed to be a blessing into a curse.
People could be fined, shamed, or shunned for breaking the rules.
The reality is that the sabbath is just a microcosm of what God wants from us...our complete attention and devotion all of the time. Every day. Every night. Every minute. He wants continuous open communication with us. Even when we work. People often get so caught up in work and hobbies that they close a door to God. Jesus showed how it was acceptable to break the rules of the law in the name of love because love supersedes everything. The law of love supersedes human laws in God's eyes.
The image of the sabbath is a time of rest. Yes, our bodies need a time of rest but there is a much bigger spiritual picture here. The "rest" is actually a spiritual place of comfort and peace where the burdens of the world no longer chain us down and wear us out.
Knowing God and walking in the way, living according to the truth and experiencing abundant life fulfills the obedience of the sabbath.
Ultimately, it is a picture of life in the new heavens and the new earth where sin will no longer affect us in any way. But God wants us to experience that now as well.
This is just the way I see it.