Your OP missed out on our immigration system.
Legal immigration is cumbersome, difficult, oftentimes takes years and years and years of waiting if you come from a non-approved country like Mexico.
It's part of the reason people commit illegal immigration in the first place. When your life is very troubled, you often times can't wait the decade of whatever that it takes to get approved to immigrate.
Edit: You did mention it after all -- though you did not mention a potential solution of making legal immigration a faster, easier process.