It's worth noting that until about 20 years ago, capital letters did not always connote shouting in English either; in earlier decades, they rather implied importance or formality (their straighter lines were easier to carve into stone, and so they were once always used for monuments, hence the term "capital"). It was quite common to see all-capital texts from government or legal sources, and you can still find all-capital sections in legal agreements to denote emphasis. The denotation of capital letters as a method for shouting grew up along with the Internet, along with many other conventions for restoring some of the flavor of spoken language to a pure-text medium.
There are plenty of other ways to show shouting in Japanese. Size, font weight, and exclamation points handle the job very well, and of course you can just add auxiliary text to say that a character was shouting. On the Internet, you can add additional emotion by emoticons: (ノಠ益ಠ)ノ彡┻━┻ or (」゜ロ゜)」 can denote anger or despair, for example. Manga adds a lot of additional conventions, such as gigantic, page-filling letters, jagged type, angled snipes around the letters, enormous mouths, etc.
Capital letters, however, are not one of the options, since there aren't any.