In economies that don't exhibit large inter-sectoral productivity gaps or high and persistent unemployment, labor displacement would not have important implications for economy-wide productivity. In developing economies, on the other hand, the prospect that the displaced workers would end up in even lower-productivity activities (services, informality) cannot be ruled out.
There is a parallel here with some of my attempts to model the Recalculation Story. When productivity goes up in some sectors, displaced workers end up in lower-productivity activities--unemployment.
This is an easier story to tell if you do not know any economics. Once you know economics, it becomes harder.
(a) When productivity goes up in one industry, why doesn't that industry simply expand so as not to have to shed workers?
Rodrik's answer in the case of developing economies is that those with a comparative advantage in resource extraction do not have that option. In resource extraction, higher productivity means that the same rate of output can be sustained with less labor, but that does not mean that you can use the same labor to get more output. My answer in the case of an advanced economy is that demand is not sufficiently elastic.
(b) when workers are shed in one industry, why do they not find themselves employed productively elsewhere, perhaps at a lower wage?
I think that the answer is that there is a shortage of entrepreneurialism. In developing countries, that shortage may reflect problems of culture and governance. In an advanced economy, the new patterns of production that must be created are highly complex, and the skill sets required may take a long time to develop. It may not be possible to shift the same workers out of excess-labor sectors into expanding sectors. Instead, the transition may involve workers with obsolete human capital exiting the labor force, with new vintages of labor gradually filling the expanding sectors.