This discussion sounds like a fun one.
There's more reasons why spears were the predominant tool for your average army in the relevant time periods, and that's training large groups of people. It takes a LOT of training to get really proficient with a sword, unless you're doing what the Romans did and using them in conjunction with a shield wall and using a very limited set of moves. Spears are cheaper to produce and don't require nearly as much proficiency to be useful, although it's VERY challenging to march in formation with a large spear. More, anyone could make a staff, which meant a lot of conscripts already had a skillset that would translate over nicely to spears.
With regards to the relative goodness of katana vs other weapons, that's very much overblown by Hollywood and other internet crap. Katana are nice weapons, and certainly have their place, but when you look at what sorts of things katana faced, they're very specialized weapons, designed mainly for use against unarmored opponents. Shields don't seem to have been popular for the samurai, so the things a western blade, for instance, had to defeat were pretty different than what a katana might. Katana aren't very versatile, realistically. They'll fail against an armored opponent, and aren't any faster than a good saber or a rapier, or even a longsword. Too, the guards are tiny, and considerably less useful than a western guard in a clinch. They're elegant and stylish, but I don't see them being inherently better or more versatile weapons than many other swords. Katana do NOT defeat thin plate or chain mail, as a general rule.
The variable temper point is silly as well, especially in a modern setting. It's certainly an elegant solution to maximizing the potential of certain types of steels, but the quality of modern steels has made the variable temper largely aesthetic. We love hamons, but a good through-tempered blade can be as strong or stronger than a variable tempered blade. I'd take through-tempered 3V over most, if not all, variable tempered blades.
The truth of the matter is, you'll be hard pressed to find an expert that actually DOES believe that the katana is the pinnacle of sword design. It's pretty well documented that it's not. For instance, when the Mongols invaded Japan in the 13th century, the samurai found that their swords were utterly inadequate against the tough leather armor of the invaders. They were forced to adopt simpler and broader temper lines to cope with that challenge. In fact, by the 15th century, the demands of war had forced Japanese swordsmiths away from the artistic nature of their golden age (the Kamakura period), and the advent of firearms cemented the demise of the katana and the way of the Japanese sword.
More, the experts I'm familiar with consider the koto blades to be the pinnacle of Japanese sword-craft, NOT the tachi that spawned the more familiar nihonto most of us call katana.
As for modern utility, a long sword, like a spear, isn't actually good in close quarters, such as the aforementioned hallway. And frankly, I'd take the spear any day. You're gonna be hard pressed to get past a spear in a hallway to the point where you'd even be able to use a katana. I'd also probably take a long knife, because there's a lot more flexibility with what you can do with it due to the shorter length. The spear is designed for quick thrusts, and a katana (or any other long sword) is too long to be able to generate force in a suitable direction for cutting the head off of a spear in a hallway. Try it sometime with a friend and some fake weapons. Your friend doesn't even have to be particularly trained. They'll figure it out quickly, and even a skilled swordsman will have a tough time closing on a spear-wielder in a hallway.
If swords were really that useful in modern combat, consider why use of such has almost entirely died off (although the knife still remains).
Don't get me wrong. I love swords, and prefer to make longer blades. And I would absolutely use one in a SHTF situation if for some reason I wasn't able to use my firearms.
But there's all kinds of fallacies in the above opinion. While sure, most opponents would be unarmored, a sword WILL be defeated by anything that will defeat a rifle bullet (duh). And reach matters. If you really think a sword is so great, I'm willing to bet you've never fought a spear-wielding opponent with one. In fact, if Musashi Miyamoto was actually defeated, his only defeat came at the hands of a staff-wielder. Skill levels being equal, in my experience a spear wielder will beat a swordsman most times. I've had several matches in my martial arts training using a sword against staff and spear both. It's VERY challenging to get close enough to hit your opponent, unless you can maneuver them into a situation in which you can use the length against them, or unless you're fast enough to grab the spear on the shaft without getting stabbed, which isn't an easy task.
My biggest issue with the aforementioned article is the lack of portability of a spear. You'd be a total fool to be toting a spear around in a post-apocalyptic situation, in my opinion, if only because of how much it would limit your mobility. Hard to climb or run with a spear, for one.
As for the "you can't shoot every bullet" argument, let's be honest. Sure, there are lots of bullets. But the odds against YOU having individual access to all of them are negligible at best. Most of those bullets and black powder weapons are going to be in the hands of other people, who may not mean you so well. Running out of ammunition is GOING to happen. Look at it now. You're right. There are billions of bullets out there. And yet it's almost impossible to find .22LR, and 9mm isn't much better. The ammo may be out there, but that doesn't mean that you have access to it.