This just sounds like autocracy with extra steps.
Maybe Joseph Smith would have done an admirable job of being in charge of something like this, but a lot of his time seemed to be take up with sealing three dozen women to himself. Brigham Young's long reign might have approached theodemocracy, but it largely just looked like low grade tyranny where you had to take up your civic disagreements with God. It's a republican government with the prophet getting an ultimate veto power and then leading the press corp and legislators in another sing-along to "Follow the Prophet, He Knows the Way."
In the Wikipedia article we get information like:
if consensus could not be reached, then Smith would "seek the will of the Lord" and break the deadlock through divine revelation.
Surely, there is no way
this could go wrong.
On the day of the council's organization, John Taylor, Willard Richards, William W. Phelps, and Parley P. Pratt were appointed a committee to "draft a constitution which should be perfect, and embrace those principles which the constitution of the United States lacked." Joseph Smith and other council members criticized the U.S. Constitution for not protecting liberty with enough vigor.
The "Liberty" which Joseph wanted to protect with "vigor" seems to be plural marriage and creative land deals. This sounds like when people defend the Confederate States of American claiming that they simply wanted to preserve "states rights." Unfortunately, the first right they wanted to preserve was to remove all rights from slaves since they owned them.
Unless it's Jesus Christ physically occupying the Oval Office, I prefer to keep the courthouse, counting house, and church house in entirely separate buildings.