First, Blackstone had no "theory."

Second, the foundation of law in the "west" is common law which grew from ancient practice of leaders/rulers exercising a "divine right" to judge disputes. The division between the "throne" and the "judge" grew over time, with the Magna Carta representing a mythical transformation from a king determining justice based on his personal interests to one of independent judges deciding issues on the basis of facts and reason. Over five centuries, England has develop a body of history that recorded the reasoning behind common justice. Blackstone merely sought to organize that history in a coherent reference.

Third, English common law was the law of the English colonies. Blackstone's Commentary was published concurrent with revolt and insurrection in the English American colonies, which placed those with knowledge of the practice of the law outside society (few members of government seek to overthrow the government they are part of - they might seek to control the government, but not to destroy it). Thus, the traitors to the crown needed to bootstrap their own judicial system, and Blackstone was the handbook for this. More copies of Blackstone were sold in the English American colonies than in England.

Blackstone is significant because he marks the point where the law became independent of the government that ruled the people and territory. He wrote of the separation of the law from religious text, as well from the king. Blackstone didn't change the practice of law, but only noted the transformation.

For the US, Blackstone is significant because his record provided access to the history of case law and the framework for the law and its application to the people who needed to bootstrap their government, and today he is significant because he provides the most comprehensive record of the law at the beginning of the American 19th century and the end of the 18th.

Blackstone's Commentary is a snapshot of the law of the English times, and the law of the English had separated from the church. This was understood by the people of the times who wrote the US Constitution, but the fear that this principle along with many others would be ignored by the mob of democracy resulted in the call for a bill of rights.

That said, religious texts were like all other records of history, assumed to be sources of precedent on which common law is founded. And the US Constitution merely became, and is, one of the historical records used in common law to find justice. Blackstone is relevant because it is as much a part of the historical record as is the US Constitution.