Having lived in Japan for 3 years and experiencing a lot of their culture, I've learned that the reason anime characters yell their attacks is because it promotes a fair, honest fight. Japanese people love friendly rivalries, and the only way to truly prove yourself better than your opponent is to give them every advantage and still come out victorious. Only a truly bad person would try to sneak in for an attack and catch their opponent unprepared. And that won't settle any rivalry, even if they won the fight.
Ninjas are typically silent assassins, not badass anime protagonists. (I'm looking at you, Naruto!) Their deeds are not generally honorable in nature. Historically, they're seen as more of an unfortunate necessity to preserve dynasties. The honorable warriors are the samurai. Although history has shown that the whole "way of the samurai" thing was actually made up for Japanese theater and they weren't historically honorable either.
Regardless, when it comes to modern-day Japan, they love the concept of an honorable protagonist who wins by sheer willpower, even if the odds are stacked against them. Giving their opponent the advantage and then still winning in the end is seen as a clean and respectful victory.
My thought is that it helps the audience know what exactly they're doing. Not saying it's necessary because I think a good visual indication will let the audience know, but I think that's what they were maybe going for.
I really liked YuYu Hakusho for having big title cards whenever some characters would use attacks (and sometimes equipment/weapons) without yelling. It was also nice that the narrator would sometimes explain things quickly to not detract from the action, though they stopped doing that pretty early on, presumably because they assumed the audience would have a better grasp on things as the show progressed, or because the characters actually had a reason to assess or explain things.
The ol' Brock effect, a character who's job 90% of the time was to tell the audience what was going on. More forgivable in a kids show, used to happen way too much in more adult shows too
I like how in JJK it's a chance to create variation in power levels while also allowing an in-universe reason to expo-dump about a character's power.
It makes a shonen trope feel like these genius characters aren't just giving away all their tricks for shits n giggles. But then sometimes we just get a total lack of explanation and that's fine too because it's more fun, and the character doesn't need to (cough Sukuna)
i think my hero academia sorta does this? i know the protag at least has to concentrate and think in a certain way to manage to pull fancy moves off before he internalizes the activation and can really do it at will, and i think other characters have similar challenges?
"so clench your buttcheeks kid, and yell this from the depth of your heart: SMASH!"
If you call out the name of your attack, you better hope your opponent doesn't know what it is, cuz it seems pretty easy to block or dodge something you know is coming.
my favourite take on this is to have characters fighting in groups, then it becomes obviously necessary to call out moves so others know what's going to happen and can know to not stand on the other side of the enemy that's about to be showered in flame.
it also makes a nice contrast between solo fighters and those who simply don't care about collateral damage: some villains can be pure chaos, you can have rogue heroes who just end up hurting innocent people because they don't coordinate, and villains who do coordinate will look way more threatening because they aren't hurting themselves.
Oh, it does! Tried it, once, very drunk, many years ago (many!), screamed something like "in your face" (actually German: "in die Fresse") and he was out cold. Only medium knuckle pain, I'm not a fighter, so I thought it did something. Don't worry, he earned it, believe you me.