If they're self-taught, I don't think they'd hold up much against people taught by people who actually know what they're doing. Unless magic learning is involved.
You're both overestimating the value of martial arts and underestimating the value of self-teaching. The reason why martial artists are more dangerous in a fight, in real life, is largely due to the physical difference born from training, which is a heavy physical activity. A person that hones their reflexes, stamina and strength through any means to a degree greater than a given martial artist is going to pose a serious danger to them even without any martial arts of their own.
Some martial arts do offer a significant edge by teaching to make the strikes more instinctive (and thus faster and more precise), other teach atypical methods that excel in certain circumstances (for example, throws or holds that allow to use your strength more effectively). But in a fight to the death, basic physical abilities, mental state and weapons are significantly more important.
Also, some of the modern martial arts are actually a detriment in a brawl. They are sports, so they are meant to NOT hurt the opponent (too much). That would make you actually weaker against any opponent that wants to just take you down no matter the cost. Training them still increases your basic physical abilities though, but so does street brawling, so a guy that spent half his life fighting no-holds-barred will more often than not completely wreck a sports-learned martial artist.
In stories with adventurers, those are usually fights to the death (especially against monsters). At that point martial artists actually get significantly less important as your main priority is hitting the opponents vital points. Usually that would be joints, neck, eyes, ears. Speed, strength and accuracy are vastly more important than any style.
Do you have a source for that? Most martial arts came about due to training for warfare and combat.
Most (non-weapon or common weapon) martial arts actually were invented for basic self-defense. Over the course of history, many countries had castes that were not allowed or could not afford any weapons. Meanwhile, those were dangerous times. As such, the peasants had to learn how to use their bodies more effectively if they wanted to have an edge if attacked. That's why there's a number of weapon-based martial arts that are derived from stuff that a peasant may have, basically farming tools, knives, most importantly sticks and staffs that never were banned anywhere (until basebal bat bans).
For martial arts using weapons like bows and swords, those were indeed largely for warfare and combat, and they were kept among nobility for very simple reason. Nobility were the only ones that could even afford to have, use and LEARN those weapons. Oftentimes, they were the only ones that were
allowed to even have them. Including out of fear that teaching plebeians how to fight would bite them in the back. If plebeians that rebeled knew how to fight well, they would pose significantly more danger to the nobles. This is the exact same logic why knowledge was closely kept, monopolized, by religions. That's why no one should be grateful to religions for 'propagating knowledge'. That's why people should blame religions for monopolizing knowledge and preventing it being spread widely, because that's what they did, just like nobles monopolized 'strength'.