Type of material decides on battery's energy density. It's just impossible for battery of "inferior" chemistry to get to same level of capacity.
There is a reason lead ones are not "just" heavy but also physically much bigger than same capacity lithium one.
What will (probably) happen if we get competitive sodium batteries is that they will phase out lithium from the stationary storage so there won't be that huge demand for lithium for everything. Or possibly they will become "cheap EV's battery"