The covenant model is merely a template by which to describe the reality, and may be discarded without loss to the traditional Baptist position. Even without any covenant, Adam’s sin would have been just as wrong and just as worthy of death (physical and spiritual). Since sin naturally enslaves and corrupts, then Adam’s sin would have corrupted his nature and enslaved him whether or not there was a covenant. And since the nature of all men was embodied in the single man, Adam, when he sinned, then that nature would be propagated to all men in its morally corrupted, spiritually dead condition—even without any covenant. Because of this, all men justly “inherit a nature and an environment inclined toward sin.” So you see, while the covenant model serves as a good way to explain the reality, the reality itself does not depend on the covenant.
In the early Reformed church, federalism did not exist. The Augustinian idea of a participative union in Adam prevailed, such that it was taught that Adam’s sin was imputed to us because it was ours. Even after the federal/covenant idea became prominent, it was held in conjunction with the old Augustinian idea, so that the justice of designating Adam as our representative was grounded on our participative presence in him. In other words, the sin still belonged to us prior to the federal imputation, and the covenant only served as an aid in understanding the reality. Only from the 18th century did the federal idea completely replace the Augustinian, resulting in the teaching that the sin of Adam was ours because it was imputed to us. Under the Augustinian idea, the corruption of nature was inherited as the natural and just consequence of our participative sin in Adam; but when the federal/covenant idea was used to deny the reality instead of merely explaining the reality, the corruption of nature became the penalty for Adam’s sin that was sovereignly put on us without any just ground in reality. In short, the reality was lost sight of, and replaced by nothing more substantial than an arbitrary decision. As long as the reality of the participation of the nature of all men in Adam’s sin is affirmed, then the Baptist faith needs no covenant theology.
Ken Hamrick, 2013