If good guys can get on board with guns, why then the bad guys can do the same. Ten terrorists can board the plane with their guns, and highjack it pretty effectively; or one loony or suicidal fanatic can board the plane with his gun, and kill a lot of people and perhaps even bring down the entire plane.
Ah, but won't armed passengers stop them? Maybe, but it's quite unlikely. First, few law-abiding passengers will go armed; in states that allow law-abiding adults to carry concealed, only 1 to 4% of all people get licenses, and I suspect that even fewer people actually are carrying lawfully at any particular time.
This analysis is right, under the assumption that the boarding regime is rather like today, but with no metal detectors. On a plane with 200 people, perhaps only one or two would be armed. If hijackers can get on armed without trouble, then they can just bring four guns and they can win (see Eugene's piece for more on that).
But I would not assume only one thing changes. In fact I would not even assume that metal detection goes away.
Here are some strategic reactions the airlines could use to minimize the number of hijacker guns on board, while increasing the number of concealed carries:
(1) keep screening for metal. If you have a gun, you must have a license and/or you must appear in a database of faces of people thought to be reliable. Big brother? Yes - but it should be the airline's right to carry who they want.
Incidentally, the scattering of a substantial number of positives in with the stream of negatives should help the alertness of the screeners a lot.
(2) If not enough passengers are carrying guns, offer incentives. Half price tickets, but only if you agree to carry a gun onboard using airline-approved frangible ammo.
(3) Few passengers will want to take a gun somewhere if they expect not to be able to use it there, which will depress the number brought on. So, set up a system to provide a handgun and concealed holster, just for the flight. The passenger must, of course, turn it in at the endpoint, where it will get reused (or just sit until his/her return trip happens).
The point here is, that what the airlines want is obvious: lots of cheap air marshalls, and minimal gun-armed hijackers. They can, and should, act to get them, if they are free to do so.
Of course, the ideas just discussed may not be the best, most cost-effective way to guarantee security. They are just what I thought up in 10 minutes. The only way to find a high quality solution is to let the market search for it. But this market is not free at all, and not likely to get that way. And that's the problem with one-size-fits-all government monopolies, like airport and airline security.