As in, illegal immigrants can be seen as good targets for crimes of one sort or another? If so, then we should say that a lot of folks are causing similar problems: by driving particular cars, having particular things, etc. Regardless, you just said "causing problems", and home invasion is a bigger problem than folks being considered good targets for home invasions.
Yeah it kind of makes more sense to kick people out who are here illegally over the ones who aren't. By sneaking in, they are criminals already.
Technically, we don't generally deport folks for committing crimes of one sort or another. It could be said it makes more sense to kick out illegal immigrants due to the fact that they aren't citizens, but doing as much en masse would cause far more problems than it would fix.