Answer is;
...YES.
We should take over Mexico starting with the contiguous ones along the border and annex them.
These states will become buffers where the residents are citizens of their states and will become the melting pots that Texas, Arizona, New Mexico and California used to be. These states have become overwhelmed and are losing the traits that made them so attractive to immigrants and such wonderful places to US citizens.
You can live and work in the US but you are resident to these states and therein lies the benefits you accrue; retirement, major health care and education. We create incentive for an immigrant to leave his family behind to grow up in surroundings that are at once of his culture yet are also transitional in nature; teaching English. Learning the US Constitution, customs and history.
Dad goes off to the US for the wages. The incentive to drag his kin along and swamp US social services is simply moved from here to a buffer melting pot. He comes home seasonally or quarterly or annually to visit and remain part of his heritage.