Another sacrament question

So it’s received wisdom that the sacrament is a weekly renewal of the baptismal covenant. But where in the world did this idea come from? I mean, the sacramental covenants (as given in the prayers themselves) and the baptismal covenant (at least the hint of it that we get in Mosiah ch. 8—it’s always vaguely annoyed me that the actual content of the baptismal covenant is never laid out at all directly) are pretty similar, but why can’t they be separate? Seems to be it cheapens both of them to pretend that they’re the same thing.