"Authority" is a word that has suffered some redefining, to the detriment of both church and state. It is readily viewed as "power over something or someone else," and includes privileges such as the right to compel and control others. This has become the accepted understanding of the word, and therefore all our churches and states function accordingly. Those who have such "authority" are viewed not as oppressors, but as "benefactors" (Luke 22:25). The Lord evidently finds this understanding offensive, and would have His people act otherwise (Luke 22:26-27).
I think a better understanding of the word "authority" in scripture would be "power to correctly serve." For example, to have authority from the Lord, one must receive from the Lord a commandment, so they might "serve" Him by executing it. They must have a correct understanding of that commandment, or they may take some course of action which actually doesn't align with the commandment. Having the commandment, and the proper understanding of how to accomplish it, they are empowered to act as an authorized servant, so long as they respect the parameters they've been given. When they act accordingly, the Lord takes responsibility for the performance, as the "author" who "authorized" the servant to perform it.
If an "authorized" servant performs their duties incorrectly, those performances are considered unauthorized, being out of harmony with the bounds of their authorization. Then the servant, rather than the Lord, is accountable for what they've done, potentially even surrendering the "authority" of the one they claim (D&C 121:34-37).
If the Gentile version of authority will not be welcome in Zion, then the economy of Zion will not function through compulsion, enforced by some police force. The people will not be living the law merely out of fear of some external consequences. Instead, their hearts having been refined and found worthy, they will have accepted the covenantal law as a matter of personal conviction, stemming from their inner desire to care for and serve man and God. They will be self-governing in a fashion, as Joseph Smith sought to inspire among his people.
This is not to say that there will be no punishment or consequence for the breaking of laws. When a people are under an actual covenant with the Lord, the Lord certainly brings about punishment unto the unrepentant. Consider the story below, in which Ananias and his wife had covenanted to live with the people under the law of "all things common" (established in Acts 4:31-37):
"BUT a certain man named Ananias, with Sapphira his wife, sold a possession, And kept back part of the price, his wife also being privy to it, and brought a certain part, and laid it at the apostles' feet. But Peter said, Ananias, why hath Satan filled thine heart to lie to the Holy Ghost, and to keep back part of the price of the land? Whiles it remained, was it not thine own? and after it was sold, was it not in thine own power? why hast thou conceived this thing in thine heart? thou hast not lied unto men, but unto God. And Ananias hearing these words fell down, and gave up the ghost: and great fear came on all them that heard these things. And the young men arose, wound him up, and carried him out, and buried him. And it was about the space of three hours after, when his wife, not knowing what was done, came in. And Peter answered unto her, Tell me whether ye sold the land for so much? And she said, Yea, for so much. Then Peter said unto her, How is it that ye have agreed together to tempt the Spirit of the Lord? behold, the feet of them which have buried thy husband are at the door, and shall carry thee out. Then fell she down straightway at his feet, and yielded up the ghost: and the young men came in, and found her dead, and, carrying her forth, buried her by her husband." - Acts 5:1-10Zion will have laws, and laws are nothing without consequences (2 Nephi 12:3; 2 Nephi 9:25-27). But this does not mean men will have and exercise power over one another, or create institutions to engage in such behavior. Instead, we would be living under the Lord as our Governor and Judge, who will be free to bring punishments to bear where repentance is absent.
UNTANGLING COMMON PROPERTY
In my view, some of the greatest fears of ultimately shifting away from private property to common property are derived from observations of the failed efforts in this world. Not just failed, but corrupted.
For example, both Socialism and Communism, two of the dirtiest words you can say to many Americans, were built upon foundations of fear and compulsion. Government was given tyrannical power, which they wielded (and still wield) like a hammer and sickle against their own people. In these brutal forms of government, they teach a theoretical embracing of some form of common property, while practicing something else entirely.
In practice, the government effectively owns all the property, and is "gracious" enough to allow the rest of the people some small portion for their use, so long as the people don't offend the government. The people have never really owned the property. If you offend the government or are perceived as a threat to their power, then fear, pain and death are used to try and get you back under their thumb. The more friendly you are with the government, the greater portion they might allow you to hold, in their behalf.
What Socialist and Communist regimes have done is pollute the idea of "common property" by association; association with brutal force, lying, corruption, oppression, murder, and every other vice found in man's societies. The regimes have spoken of the people being one, while they have always been definitively two or more: government, and the rest. That is not "one," and therefore it is not Zion.
As this is pretty much the only way most people have seen a government attempt "all things common" or something like it, the idea becomes enmeshed with fear, oppression and death, and nobody wants to participate in such a society.
But seeing as no versions of these societies has ever actually practiced "all things common," in spite of lip-service to the contrary, what if that concept can be extracted from entanglement with those societies? What if those corrupt societies were designed as they were precisely to make a mockery of that principle, to convince us by association with evil that "common property" must be bad? What if they represent Satan's best efforts to mock the model of Zion, saddling it with all his worst compulsion and fear, to convince us not to consider "all things common" divorced from fear and compulsion?
What if "common property" isn't actually the problem, but the lack of refinement and preparation of the hearts and minds of those who attempt it? What if in such corrupt societies, neither the governing nor the governed were sufficiently righteous and prepared to adopt such a weighty idea? As evidenced further by the fact that the Lord never invited them to enter into that model?
What if a people were prepared sufficiently in their hearts and minds before attempting such an endeavor, could it be possible to live such a law? Just because we haven't had the opportunity to directly observe such a model in this world, doesn't mean it is impossible for it to come forth. Our scriptures point to it having happened in the past, and happening again in the future, among a prepared people. But it will be unlike any of the models we currently see.
"The government of the Almighty has always been very dissimilar to the governments of men, whether we refer to His religious government, or to the government of nations. The government of God has always tended to promote peace, unity, harmony, strength, and happiness; while that of man has been productive of confusion, disorder, weakness, and misery." - Joseph Smith, TPJS p. 248