Much talk here implying this is something new! Charter flying in the early 1980s we used to have exactly the same challenge on flights such as UK to GRO or IBZ, especially the ones that left circa 2200.
These people should be denied boarding in the flight place if possible. Trouble is someone has to make a judgement as to whether someone is "drunk" or not. Ok there's the legal aspect but it's not always cut and dried. Will said passenger obey instructions from flight crew? Would this person impede exit in the event of an evacuation?
Our culture is much more alcohol orientated than it was. Should alcoholic beverages be served in the terminal buildings at all?