How does the government's disposal/burning of elephant ivory protect the market from illegal trading/poaching?
If the government destroys ivory this year, then there is less of it this year which may cause price of ivory to rise. That may dissuade some current potential buyers. (I am assuming the government is destroying ivory that would otherwise be available to the market.) On the other hand, the higher price may encourage more people to enter the poaching business in the near future. On net, most economists would argue that reducing the supply available to the market would raise prices and encourage more poaching. Since ivory is storable, a better policy might be to confiscate and store the ivory in a safe place and then release it at a later date all at once so as to cause prices to plummet. That will kill off a good chunk of the poaching business, at least the part of the business that does not have deep pockets.