It's illegal to allow drunken passengers on board in the first place (at least in the U.S.), but since there is no enforcement of this regulation, there is no obedience to it. Airlines follow the money, and if they know that regulations against drunken passengers are being ignored by enforcement authorities, and letting drunken passengers board increases revenue, they will board drunken passengers. They do exactly the same thing with safety regulations, unfortunately.
Airlines only obey laws when the penalty for disobedience is more expensive to the airline than the penalty for obedience. If the regulators actually start violating airlines for letting drunks on board, the number of drunks boarding airplanes will decrease very dramatically (in proportion to the fines assessed against the airlines by the regulators).
It's easy to prevent drunks from boarding: just issue a breathalyzer test to anyone who seems intoxicated and objects to being denied boarding. If it's above a certain level, deny boarding (zero tolerance would be better still, but that would never be accepted in a society where this type of drug abuse is so universally practiced).
Alcohol on board is also a problem, and the best way to deal with it would be to stop serving it, but again, as long as it's legal (or free of any penalty), airlines will do it. It's a lot easier to get drunk prior to a flight than during a flight, however, since the quantity of alcohol that can be consumed pre-flight is much greater.
I seem to recall that alcohol is a factor in at least half of all on-board incidents, but I can't find a reference right now, so I might be wrong on that. Another factor is that extremely low airfares have allowed increasingly immature and ill-behaved passengers to fly, although it's politically incorrect to make that observation.