I think the original reason they were allowed on board after smoking was prohibited was due to the fact they are unsafe to carry in hold luggage. It was safer to have them on your person where they can't accidently start a fire in the hold.
That was as a dangerous goods perspective.
Since the shoe bombing attempt numerous years ago, I'm surprised that they haven't placed a ban on carrying them. It would just mean that it is impossible to carry lighters/matches to where you are going, which I'm sure would upset those who need a cigarette immediately before and after a flight, but accomodations for those people can be made in airport smoking lounges.
As to if it is possible to police - It is no more difficult to police than the ban on liquids. The new scanning technology that is on its way shows an alarming amount of detail, almost down to being able to tell your religion
and I'm sure matches would show up
