Nope, it's a technological issue. Increasing immigration might address some of the symptoms of the issue, but it does nothing to address that a human being still needs to do this labor. Frankly even if you were to liberalize immigration laws, convincing people to upend their lives and move to a high cost of living country where cultural integration is difficult at best just to pick tomatoes is not exactly a trivial task. Even if you do get people to come for menial labor, as you say there are plenty of other areas like healthcare where labor is in high demand, so you're likely still going to be faced with labor shortages in less desirable fields. Immigration is a treatment, automation is a cure.