The government in Mexico has always been corrupt, and our government has usually tried to pretend they weren't and dealt with them on that assumption. (Why, I do not know)
The officials used to be bought off, now I think they no longer have any power, no need to buy them off. Drug lords are in control now, and each has their own area. There are drug wars all over Mexico to determine who will control each area. I don't think the Mexican gov't has to help illegal traffic any longer- I don't think the smugglers need the help any more. That is why I have come to the conclusion Mexico is the new Columbia. There are mass desertions from their Military, and LE. The deserters are joining up with the Mexican "mafia" gangs and drug lords. Military and LE over there has always gone to the highest bidder but now they are not even pretending to be honest.
To answer your other question about what they export to the US other than illegals and drugs; the answer is oil, and many products made by former American companies who moved south of the border. Vegetables are imported also, and of course a variety of tourist related items. As far as I am concerned, they need us worse than we need them, no matter what they export.