I remember World's Mightiest Disciple where people did go to the hospital but they were SO incompetent that a Chiropractor and a Acupuncturist were far superior.
Which is fine in an anime about how these dudes are basically some of the greatest people to live.
But GOODNESS the things they heal that hospitals miss are staggering. In one case they heal a pinched nerve that the hospital, that specializes in those kinds of injuries, misses.
So pretty much after that no one went to the hospital anymore... even for life threatening injuries.
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Though I love anime. For every trope you can find examples and counter examples... Ones that do it right and ones that do it wrong on both sides.
For example the "Yakkate Japan" does the "Super Genius" right. You see where he got his skills from and everything he does stems from it while also having a natural talent for it so you get the sense that he actually worked very hard to get where he is. While Master Cooking Boy is the exact opposite where our hero's skills and abilities are mostly completely unexplained and he just has talent out the wazoo and mostly doesn't work too hard.
While the opposite end you got the main character from Yamino Pastichie who at no point ever gains a "talent" for cooking, she is "creative" but only on a above average level... and while she has the super sense of taste it never comes into play except all of once (she never uses it to make better dishes). So everything she learns is entirely through effort and her detriments never just disappear, as well the traits that usually allow her to "win" are all personality traits. For example she is very considerate and caring.
While the opposite and got it wrong is World's Mightiest Disciple where our hero is "talentless" except he really isn't... who works like crazy, but not harder then anyone else really, and is better then anyone else and we are constantly informed about how "not talented" he is. Essentially he is a Harem Comedy protagonist except replace his "Can't get women" (Which obviously translates to any woman who spends more then 1 hour with him will fall madly in love with him) into "Sucks at martial arts". It isn't that they don't try explaining it away, it is that they try hard to completely discredit the hero and say it is "all effort" when what we see doesn't back it up... especially when "boundless endurance" and "Unbreakable will" are both great martial arts talents.
Now let me see what Western shows are on right now... Ohh... the only... non-comedy show on right now... is absolutely dreadful... well thanks TV. Wait there is Legend of Kora! yay!