Having worked at two manufacturers in the Midwest, anecdotally the majority of forklift drivers, line workers on specific lines, and even many white collar office roles were filled by temp agencies. A similar structure existed for engineering too; we would have a problem and the engineering firm with workers under the same roof would develop a solution.
For the temp workers the motivation was always very clear and very much based on working around labor laws. If a forklift driver got in an accident, it wouldn't be counted in the same way. Line workers could be less rigidly brought on board or let go with seasonal or other varying demand. They were cheaper too and everyone worked hard to try and become a regular employee.
I am not sure what a solution is, after all these types of temp companies only exist to skirt existing labor laws, suggesting these laws may defy economics a bit too much. On the other hand what other ways do we have of increasing the bargaining position of labor? Growing the economy, but that isn't something a politician can honestly promise. Pulling back from globalization would, but that is bad economics and bad for national security. Perhaps something like earned income tax credit? Or perhaps we should just continue waiting until the rest of the world develops and the supply of labor finally becomes constrained.