To give a super blunt answer..
Japan's history kinda hinges on conformist ideals, and individuality is kinda frowned upon. There's a famous old proverb about it, "the nail that sticks out gets hammered down"..
To go into it slightly more and do some generalizing...
It's not even that they're competitive with other countries, quite the opposite actually- Japan tends to be quite isolated and holds themselves to such high standards. If everyone in the country is expected to be like other outstanding people in the past.. there's not really much room for one person to be themselves, especially when the high standards have been shown to function well everywhere else in the country.
Anime and manga happen to be a result of being influenced by Western media. As such, characters can be exaggerated just like in Western cartoons and comics. This also happens to be an outlet for writers and artists, so any repressed emotions are basically allowed to come out onto the pages and animations.. this extends to gaming, cinema, music, any creative field really.
Japan's emotional side is often reserved for media that won't negatively impact anyone else in the real world. The reason for that being, their history and the morals they pass down through generations. That's not to say you won't ever see people smiling or crying or even showing affection in Japan, but people are very mindful of others in their country. The mindset seems to be "if an emotion is gonna inconvenience someone, it's best not to show it at all."
(anyone else more educated on this, feel free to correct me or add on to what i said)