Assimilating mexico would add 100million people that are used to living in third world conditions to the US. This would be a disaster for our economy, criminal justice system and society
The impact they are having right now on those sectors of our country are identical to your "worst case scenario" portent.
The lawlessness and other problems associated with the Territories of the US were eventually all but destroyed by the assimilation of the Territories into the USA as full-fledged States.
This is the solution I see for Mexico. Their government and people cannot and will not do it for themselves and they will forever be a problematic thorn in our side.
They are a very real threat to our nation in their current incarnation on multiple levels of analysis. They must be stopped because they won't fix themselves. They've proven that every election cycle since their inception.
The solutions to the Mexico Problem are simple and limited in number:
(1) Do Nothing; Let the situation persist
(2) Invade Mexico, annex all territory, dissolve government, rebuild interior under US State model
(3) Build Wall with armed sentries and detection equipment, killing those that attempt to cross and deporting those already here, regardless of citizenship status, as long as Mexican-ancestry or Mexican-sympathizing can be established
(1) is going to be the likely choice
(2) is the best solution for both nations
(3) is even more of a pipe dream than #2