In light of the evidence produced by mainerjohnthomas and a_majoor, I'm definetly willing to concede that a rifle/bayonet combo is useful for crowd control situations. As such, I will revise my position to say that bayonets are obsolete for anything other than cowering unarmed crowds of protestors.
Consider a second scenario, you confront an intruder with a .22 pistol or a 10gauge shotgun; I can shoot your eyes out with the .22, but it is unlikely to inspire enough fear to make the intruder run, I will HAVE TO SHOOT, the visual impact of the shotgun will make the intruder (more often than not) think twice and beat feet.
Thank you, I think we're hitting the crux of the debate. There are two schools of thought WRT to your scenario which can also be applied to crowd control situations, both of which have merits.
Your school maintains that the sound of a shotgun being racked is often enough to scare away intruders, and in this respect, a shotgun is more useful than a pistole for bedroom defence.
However, there is also another school, towards which I lean, that believes firearms of any sort should never be produced unless one intends to use it. What if the intruder also happened to be armed? More importantly, anyone in a self defence scenario must be in the mental state which has only one purpose, that is, the elimination of the threat at all costs. Any kind of halfway step will be counter intuitive to the stated purpose. Flashing a bayonet at a crowd will certainly be intimidating, but it only takes one schleevo soaked sod to make a grab for the rifle. Could there then be a situation where you would want to actually bayonet the guy but not shoot him? Unlikely I say.
I must disagree with your comparison of the bayonet to the MBT. 60+ tons of fire-spewing depleted unranium is definitly a tad more intimidating than a bunch of guys with pointy sticks.
Ultimately, we must always keep in mind that everything is a trade off. Having a bayonet means having less ammunition, a fact often under-appreiciated by those who do not regularly train with armour and support weapons, there's no way around it.
I cannot understand why "if I run out of ammo" is a good reason for bringing a bayonet. Your bayonet is not ammo, why didn't you leave it at home so you could carry MORE AMMO? Or take the time you spend poking sandbags and spend it on improving your marksmanship?
Lastly, while you certainly can wave your bayonet around the air indefinetly, you'll find that the bayonet has a much shorter useful life if you actually start poking things(like hard surfaces, for example) with it. Not that it would make much difference, since you will most likely be swiss cheese at that point anyway.