It’s difficult to know how far back in time the keeping of the sabbath day as a holy day, different from all others, can be traced back in the Old Testament. It probably doesn’t pre-date the exile in Babylon. Perhaps it was while they were living in a foreign land, and desperately trying to remain distinctive from the people and cultures around them, that Jewish people started keeping the sabbath and formulating the sort of traditions which come down to us in this passage.
Even after the return from exile, and the publication of the Book of Exodus in its current form, keeping the sabbath was clearly not a universally popular idea. The two harsh warnings about putting people to death for breaking the sabbath commandment show that many of them must have been seriously tempted!
In Jesus’ time the struggle between sabbath observers and sabbath breakers was clearly still going on, with the scribes and pharisees seeking to enforce it in the face of a lot of indifference and outright opposition. Jesus himself opposed its strict observance, pointing out that one of the justifications which Exodus gives for the sabbath commandment is humanitarian - the sabbath was instituted for our benefit, not simply for its own sake.
Notice that this objection does not rule out sabbath keeping or even seek to delegitimise it. Jesus mostly chose to keep the sabbath too, but he allowed humanitarian considerations, like hunger, illness or need, to override the obligation to keep the sabbath holy. In point of fact, so did his opponents, but he was just more lenient than they were. He felt it was legitimate to heal someone on the sabbath if they were in pain, whereas his opponents may have felt that it was only legitimate if someone was at the point of death.
In the end, of course, a fairly strict pattern of sabbath keeping prevailed, partly because Jewish people found themselves in exile once again and partly because it was now one of the things which most clearly set them apart from the new and growing Christian community. But even Christians can agree with the writers of Exodus about one of the reasons for keeping the sabbath holy - as a reminder that really everything is holy; that our world belongs to God, and was made by him and that our work and our rest should honour the creator and complement his mission to make the world a perfect place to live.