My wife asked me a similar question. Having Moses speak God's commands/words to the Elders, and then to smaller groups; seems a quite reasonable explanation. We have a similar situation with Moses exhausting himself--settling disputes. Far too many people. His father-in-law gave wise counsel: Delegate! No need to do it all yourself. Regarding the supernatural explanation--I agree; this was a time of God making his immediate presence known to the whole house of Israel. (If one a-priori rejects the supernatural; one would reject the parting of the Red Sea; etcetera.) No problem with God using his own means to speak to these people in the hearing of one man. Although--that does seem like a case of "special pleading." We can only infer (conclude) that God chose a supernatural means of communication. (Directly to the people through Moses.) As an aside; the (thoroughly disproved) "Assured results of liberal 'Higher Criticism'" of the Old Testament claimed--without proof--that in Moses day; "people could not write." The spade work of biblical archaeologists put that unsubstantiated claim to death.
As Nelson Glueck states, on the one hand
It may be stated categorically that no archaeological discovery has ever contraverted a biblical reference”, whereas on the other “Scores of archaeological findings have been made which confirm in clear outline or exact detail historical statements in the Bible. 
Archaeologist William F. Albright observes:
The excessive scepticism shown toward the Bible by important historical schools of the eighteenth-and-nineteenth centuries, certain phases of which still appear periodically, has been progressively discredited. Discovery after discovery has established the accuracy of innumerable details, and has brought increased recognition to the value of the Bible as a source of history. 
There is much we don't know about the twelve tribes Exodus from Egypt. Trust God. The unbiblical claims of unregenerate men eventually fall flat. The same with science. Popular; sensationalized theories today may become tomorrow's relics. The Bible is like an Anvil. The hammers of godless men have been pounding away on the Anvil for thousands of years. The hammers wear out. The Bible remains.
 Nelson Glueck, Rivers in the Desert: A History of the Negev (New York: Farrar, Strauss & Cudahy, 1959), p.31.
 William F. Albright, The Archaeology of Palestine, pp.127-128, quoted by Josh McDowell, The New Evidence That Demands A Verdict (Nashvile: Thomas Nelson, 1999), p.61.