It is legal to ask for someone's passport details, and the crew have the legal right to demand them, but it is illegal to confiscate a passport. Furthermore, what do you do when the passenger refuses to show the passport? Apart from calling the police to the aircraft on arrival, who sometimes refuse to turn up in my experience...
The best thing is to prevent drunks' embarkation, but you still face the problem of people getting drunk during the flight, either from onboard or carry-on drink. Of course, if safety was really aviation's no.1 priority, rather than making piles of easy money at the cost of safety, then alcohol would be banned from airports and aircraft cabins entirely.