Some TL;DR thoughts on immigration and technology.
For the progressive liberal, the telos of humanity is an economic utopia where ditch-digging has been replaced by new technologies born of the unfettered subsidization of science. By eliminating the old prejudices, biases, and superstitions of yore, humanity is able to leverage all of its resources in pursuit of a world without suffering or toil.
In support of this theory, the liberal points to the correlation between slavery and technological and spiritual backwardness. The reason, for example, that Hero of Alexandria's steam engine never developed beyond a mere curiosity was the ubiquity of slavery, along with other factors that were products of superstition. What need is there for investment in technological innovation, so the argument goes, when there is a surplus of slave labor to perform every task (a surplus of machines with the most sophisticated internal computer ever known)?
Setting aside the objections to this argument and agreeing for the moment that superstition and a callous disregard for "human dignity" inhibits the development of technology, let's consider another pillar of liberal dogma: cosmopolitanism and free immigration. If cheap labor inhibits capital investment in technological innovation, and technological innovation is the primary goal of liberal political action, then why do liberal policy-makers insist on flooding first world countries with cheap slave labor? Indeed, robots don't assemble SWPL I-Phones because Chinese slave labor is cheaper than the development and maintenance of robots.
But, the liberal counters, the establishment of labor equilibrium through open borders eventually increases wages overall such that investment in technology eventually becomes efficient. This also has the added bonus of increasing aggregate living standards!
Once again, setting aside the obvious objections to this argument, let's return to the basic principle that technological innovation eliminates the need for mundane wage labor. The progressive liberal's corollary assumption here is that as wage labor is eliminated, wage laborers will still be provided with a high standard of living, despite the absence of demand for their services. This corollary is merely a fanciful wish, not a logical corollary. We already know in our time that just because there exist enough resources to provide everyone with a high standard of living, not everyone will necessarily enjoy this standard of living.
Thus we are left with the other implication of technological innovation: it eliminates demand for wage labor. As investors enjoy greater returns on their capital by investing in the development of technological "slaves" rather than costly wage laborers, ditch digging labor is indeed eliminated, but so is any need for a vast portion of the bell curve that was bred to perform those duties.