Maybe a better solution is to cancel birthright citizenship and thus enable unlimited number of foreign workers? They will sign papers that exclude them from possible naturalisation as a condition of entry, and their children will not become citizens, and thus cost of doing "human work" may be kept at arbitrarily low level, fed by labor of people from countries where there is no technology driven cost disease?
In part i believe, better functioning society enabled by cheaper services as described, which we can observe in EU, are due to the fact that here in EU we don't have birthright citizenship. So there can be as many foreign workers as desired and they are not "immigrants".
Dubai is an extreme example of the same where foreign workers make up around 90% of population.