As you said, a change in immigration laws that would prohibit anyone who came here illegally from ever attaining legal citizenship would be a good step.
Most don’t care about citizenship. Most don’t care to assimilate. They just want to work and send money “home.”
It sends a bad message - if you can get to the US by any means, eventually they will let you stay. When that happens, we no longer control our own immigration.
It is also dangerous to have two classes of people. Citizens that can vote and “others” that we allow to live here but not participate in the American process.
Enforce current laws and most will self deport.