If there aren’t any immigrants to work them, either the pay will increase or the product/service will disappear. Essential services and products won’t disappear, so this seems okay?

If we look at it from the other direction, we are artificially increasing quality of life by taking advantage of foreigners who have no better option than to work for little pay. Getting rid of this seems positive?

Essential services disappear all the time. Look at the increasing rarity of teachers and the effect that has on student/teacher ratios or quality. Same with medical staff, farm labor, and dozens of other industries.

I'm not saying that exploiting immigrants for labor is necessarily good, but the free hand of the labor market doesn't usually achieve policy goals.

Teaching and medicine are both highly regulated, so not great examples of free market behavior producing poor results. Quite the opposite! Also, even the demand for teaching in the first place is drastically increased by a prisoners dilemma induced by the government, where so many kids go to school that the schools have a near monopoly on childhood peer socialization, despite the age-cohorted butts-in-seats environment not being all that great as far as socialization environments go.

Farm labor is not very regulated, but until about 10 minutes ago it was flooded with cheap foreign labor which seriously distorted the pricing mechanism for labor. And, that distortion helped to paper over some serious money supply expansion, i.e. the foreign labor helped food not get as much more expensive over time as it otherwise would have. If we keep things steady for several years we will see the market stabilize and rebalance, albeit now at a higher level (due to past money supply expansion finally being realized in prices).

*Note that I don’t really support the haphazard way this has been done, and I’m not confident that things actually will be held steady given the political environment, I’m just stating what theoretically would happen if they were.

Exactly. Any business that depends on a large easily exploited underclass who doesn't have the rights, protections, or freedoms of the rest of the population is either a failed business or one that's exploiting people to line their own pockets. In either case, there's no reason why we should allow them to do it.