They are here illegally despite your nonsense and MOST people do not want them here illegally. If they go through the legal immigration process that's quite another thing but most are in no position to do that. They are, simply, criminals.
Were they immigrating illegally into Mexico they would get far harsher treatment under the laws of that country yet that countries leaders are badgering the US to offer all sorts of "preferential citizenship status" to those illegals when Mexico itself would do nothing of the sort.
You can read about (and become informed of) Mexico's immigration policies.
Actually, wouldn't the logical solution be reciprocity between Mexico and the US since Sauce for the Goose is Sauce for the Gander?
The "blame" is - and should be - on the US government and it's politicians who are so touchy-feely it is unbelievable. Those coming here to work mostly do not wish to become Americans and most haven't the common sense (or the decency) to even make a servious attempt to learn (and use in everyday life) the English language and many are very poorly educated and some are fleeing justice in their home country. There's no reason to believe that these sorts of "illegal immigrants" are going to become model (or even productive) citizens. Instead they'll merely help trash our country as they've trashed land on both sides of the border - but especially the US side - by strewing castoffs of all types in what had been relatively trash-free public (or private) land. Why do you think, for example, that state park rangers in public land areas near the "immigration/coyote trails" now carry 9mm handguns as part of their uniform? Less than a generation ago, that was not needed ... or even considered.
If there are large numbers of illegals in the country today, and there heve been illegals in the country for many, many, many years, and they live an open life, often involved in the community, often welcomed into the community, and I can, and have, observed this with my own eyes since the 40s, then, after these facts, defacto, they obviously have some status.