Could a skilled fighter only be able to fight using one type of weapon, like a sword, and be practically useless in every other weapon or unarmed? Would being unable to fight unarmed be really dangerous in case he gets disarmed or loses the sword or is caught without a sword on hand so is neglecting to learn a really bad decision?
Hypothetically, yes, but, you’ve already identified one reason why no one would intentionally train this way. However, there are other reasons.
The mono-weapon fighter is fine for very specific archetypal stories. It’s not realistic, it’s not supposed to be, it’s a caricature. At its worst, it’s a kind of munchkining. You’re moving stats around on your character to make them the absolute best at something, and who cares if you swapped out their ability to read for another +1 To Hit while using swords?
Now, I am a fan of using RPG (or pseudo-RPG) systems to build characters for your writing. I’m also entirely fine with heavy minmaxing for RPGs where build optimization is critical to combat balance. However, minmaxing has very limited applications for actual roleplaying, and does not tend to work well for prose characters.
If your goal is a borderline cartoon character, fine. It’s not realistic, but that was never the point.
The mono-weapon fighter actually works against their stated goal. The entire idea is that the character has somehow avoided learning about other weapons while mastering one. Meaning, they don’t know how to use those weapons, and (following this logic) don’t understand what those weapons can do. Your swordsman wouldn’t know how to use or defend against an axe or spear. This is before you consider unfamiliarity with weapons specifically designed to counter their weapon of choice (like sword breakers.)
From a combat ecology standpoint, it’s very important for a fighter to be familiar with the weapons they’ll commonly encounter. It doesn’t mean they need to be an expert with every one, but they need to understand how to use those weapons, what they’re capable of, their weaknesses, and how to defend against them. That last two parts are much easier to internalize when you’re familiar the first two.
Of course, if you know how to use a weapon, even if you’re not a master, it means you can use one if your weapon of choice is unavailable.
The only place where a mono-weapon fighter really flourishes is in some kind of ritualized dueling system. If both fighters are completely restricted to a specific weapon (or weapons), and they’re all training with that, then ignoring other weapons might an option. Except, even there, cross-training still has value.
This is a little more open ended, because it’s impossible to say exactly what someone will take away from a lesson. However, when you’re training with other weapons, you’re going to learn things that will work with them, things which you might be able to translate back to your weapon of choice. A diverse education in violence will open new options, which you wouldn’t have known about if you limited yourself to a single weapon.
It’s entirely possible someone would focus their expertise into a single weapon. With them constantly working to improve their use of it. However, an individual like that would already have a background with a variety other weapons. If they use their skills in warfare, they’d also know to avoid neglecting other weapons. However, if their occupation is as an educator, a duelist, or an entertainer, it’s entirely possible they’d only focus on their weapon of choice.
Similar to your question, you also wouldn’t see serious combatants carrying a single weapon into battle. A primary weapon, sidearm, and even a backup have been pretty common throughout history. So, a soldier might start with a spear or pike, carry a sword or axe as a sidearm, and then have a dagger or hatchet as a backup weapon. If their primary weapon is lost or destroyed, they’re not unarmed, and can continue to fight, though they may want to secure a replacement for their primary as quickly as possible.
If you are going to battle, you do not want to be unarmed. Take more weapons than you think you’ll need, make sure you know how to use them. Finally, ensure you know how your foes’ weapons work, so you can defend against them, or exploit their weaknesses.