Semiautos and full-auto battle rifles came along only about 60 years ago, and even then, running out of ammo in the face of a human wave attack or a banzai charge was a real possibility.
Nowadays, however, resupply of ammo is an order of magnitude better, and an individual rifle can carry 20-30 rounds on its own. Since ammo is smaller and lighter, the individual Soldier can carry more of it, as well.
Let's not forget, also, that even IF the Soldier runs dry (A pretty big IF, there. It means that a whole lot of other things have gone awry) he can, using modern comms, call down all manner of high-explosive Hell on his enemies in short order. That's another thing...in past wars, losing radio contact was a very real possibility, as only one man in a platoon or company had a radio. Of course, now every Soldier can contact someone.
Because of all this, the bayonet has fallen into very specialized uses...landmine-hunting, poking suspicious brush=piles, and prisoner herding are some that will probably happen far more often than any thrust-and-parry work. The bayonet itself has become a multi-purpose field knife that just happens to have a lug attachement point on it (see the M-9 bayonet).
Bottom line is, it's not as important anymore as is commonly believed.
The technique still seems to have some proponents and adherents here and there, it seems. Interesting to note that it seems so useful around those who are all similarly equipped...it seems that even in their deteriorated society, when armed individuals entertain disputes, they tend to be more polite in dealing with each other than when one is unarmed and there's a clear disparity of force available.
-archy-/-