That would seem to be correct, as Samurai often trained in a variety of weapons, the most central weapon to their training was either a spear, polearm type weapon similar to a naginata, or a yumi, the longbow. As far as the steel being that brittle, it wasn't, but it was more fragile than the better European ores of the time. It would take quite a bit of effort to simply break a katana, otherwise they wouldn't have survived their first battles.

Now the important thing to realize about the Samurai is that they didn't use a chain mail--they used boiled leathers and scale mail in their armor, as it was seen as dishonorable to make yourself overly difficult to kill. A person was meant to go out, slay the enemies of their lord, and not be an unstoppable juggernaut of mail and armor, even if the o-yoroi did exist.

Samurai referred to spears and naginata as the king of all weapons, simply because of their range. The ability to dictate range is everything in combat, so the katana is definitely less suited than a spear. Of course, there's a notable exception when you start considering blades like the o-tachi and nodachi, both of which are made for cavalrymen to fight footmen and footmen to fight cavalry by killing the horses and then the men, but because of their size, o-tachi and nodachi were extremely hard for the common Samurai to use.

That said, nothing compares to the yumi. Samurai often regarded it as a rite of passage to have their sons practice kyudo and mounted archery is especially lethal. Due to the yumi's size, it was quite effective at controlling range, much more so than smaller bows of the time. This would have made a force of horsemen incredibly dangerous, and it would have also made them hard to compete with, as the horses simply have more speed and can reposition faster.

The daisho, the sword pair, were always a Samurai's secondary weapons, in the event that his spear or naginata broke or he somehow lost it in combat. At that point, the Samurai would have to draw the katana, but all skilled Samurai were trained well in kenjutsu, so its not as if it were an instant loss, but a foot soldier doesn't want to fight someone that has a naginata, yari, nunti-bo, or an eku with just a sword. Of course its possible, but first you have to close that massive range gap and force them to draw one of their daisho, either the katana or wakizashi.

That said, it wasn't uncommon for Samurai to kill each other at the same time in battle. When two Samurai square off, that's extremely bad for both Samurai, since there's a very high probability that the first movement means both of them will die, so they tried to engage in duelist contests as little as possible, with the most prominent exception being peacetime.

There's also the fact that Samurai often carried a huge variety of weapons, one in particular being the kusarigama, that no Samurai wanted to fight against. A kusarigama is a kama, a short farming scythe, on either a long rope or chain with a weight or ball at the other end. Miyamoto Musashi, by all accounts, one of the greatest swordsmen ever to live in Japan, was challenged to a duel, and as he entered the hotel in the town to wait for the duel the next day, he saw a woman practicing with a Kusarigama. When he asked one of the people tending the hotel who she was, he found out that the woman was the wife of the man that he was there to duel. Miyamoto also heard the person say that her husband was even better than she was, so Musashi simply picked up his belongings, then left and didn't show up to the duel.

Essentially something important to keep in mind is that every single weapon has its benefits and its downsides, and swords have their downsides when it comes to fighting weapons that have a much longer range or can be swung faster than the sword. A Samurai would not have been eager to challenge a master with a nunti-bo or naginata with just a katana, nor would he like to fight someone with a giant sword like a nodachi without a spear or yumi.