The cartels would not just become upstanding taxpayers and the US is legalizing weed. Anti-American comments will always get you up votes but your scenario is very unlikely.
I am quite sure that the cost of providing their own security is considerably more than any taxes on legitimate businesses in mexico. So it makes sense for them from a business perspective. Obviously it won't happen overnight. Some of them will adapt and work within the system, others will find that their old ways are not competitive with the legitimate businesses, who have lower overheads.
Obviously there will still be crime, and the cartels that don't adapt will find other criminal enterprises to pursue. But it's hard to see another market that will provide them with comparable income.
It was not my intent for the comment to come off as "anti-american". Just saying that mexico making this change would move the problem to the US, which would then be forced to act, hopefully by following through with a full-on legalisation of their own (not just for marijuana).