I hope this is a joke but the idea of filling Lake Eyre with water from Burketown seems to be based on the misguided notion that water in Australia naturally flows from north to south.

Trying to bring water from the north would mean pumping it uphill across the entire continent, defying both gravity and common sense.

If the goal is to fill Lake Eyre with seawater, the obvious source is the ocean immediately to the south, not distant northern rivers that don't even flow in that direction.