If by "underclass" you mean people that work on low value jobs - yes, these people exist and will always exist, unless you figure out how to make everyone be born with equal skills and immediately be ready to take any job and do it equally well. Then, of course, you could pay everybody the same and be content that nobody is paid below average. Fortunately, this particular nightmare society would never happen.

In real world, people have different skills, and they start with low to no skills and then develop them. In the process, they progress from low wages to high wages. When I was young and uneducated, I worked low-wage jobs like cleaning the floors in local supermarket or looking after the conveyor in local bakery. If these job were forced to have wage anywhere close to what I ask for now, these jobs wouldn't exist. And I, as a poor student, would not have a possibility to study, since I would literally have no money to buy food with, let alone pay other bills. Yes, that's how capitalism works and I'm not sure how could it work differently and remain capitalism. If you prefer the other option - taking the money to central authority and then let it provide for the food to the students, the education, the wages and so on - that's not capitalism and the experience shows that idea doesn't really work out.

That underclass work kept me alive when I was homeless. The work let me eat and keep my dignity.

If you illegalize low-wage labor, only scoundrels will hire the young and the desperate.

I don't think anyone is saying that. There's plenty of proof that lots of businesses that function...even thrive by paying people poverty wages. The question however is...is that right? Are you okay climbing to the top on the back of someone else? If you are, then you'll do well. If you aren't then your hike up will be difficult and slow.