1) Safer yes but currently it is far from easy to enter the US legally.
Well this thread is not really about legal immigration, but I will say I can agree we can make it easier for people to come here legally, but that does not mean everyone who wants to come right now can come.
2) Did the mobsters continue bootleg operations after alcohol prohibition ended?
The better question is did the mob dissolve after alcohol prohibition ended? I think we can all agree that they did not.
3) Competition makes it hard for the cartel to make a buck off it. They want a quick easy buck not a legitimate business.
Competition with who? Drug cartels could arguably easily undercut the prices of the legitimate competitors, and continue to make money selling drugs. Additionally, they do not have to run legitimate businesses persay, they can run front businesses and sell the drugs illegally (free of government red tape, taxes, licenses etc, which presumably means cheaper).