Interesting question. The EnglishWiki (surprisingly) seems better documented than the other wikis on the subject: http://en.wikipedia.org/wiki/Letter_case#History

Well, it is known that for the Latin alphabet, dual case script was a deliberate invention - it came about when Charlemagne sought to have a standard scribal hand created, and so it combined the original Roman monumental script for capital letters with a lower-case based on uncial.

According to this page,

http://learnrussian.rt.com/alphabet/the-history-of-the-cyrillic-alphabet/

lower-case letters were added to Cyrillic by Peter the Great.

And the Wikipedia article cited in the post above gives information on the origin of Greek lower-case as well. So far, I've found nothing on Armenian lower-case.

...but now I remember that a few days ago, I came across something that mentioned that Bolorgir was originally the name for the Armenian minuscule hand, before it became applied to the traditional style of Armenian types.

Before minuscules were developed (Latin), there were uncial sorts used for body text in book production. To set captions, chapter initials, certain word or sentence beginnings and similar focal points inside the text against the common style, more “ancient-style” e.g. Roman capital shapes have been employed, more or less obvious/deliberate. I think there lies the origin of a dualistic behaviour which later became a bicameral canon.

Still today the regular use of lower/uppercase is remarkably different in different languages.
But no country adopted the tricameral system of the old days as mandatory, this is the sad side of the story ;)

Sumner Stone did several presentations about this stuff years ago. His general theme was the increasing complexity of the Latin writing system, which has had letters, case, punctuation, figures, and styles (Italic, then Bold) folded in over the centuries. As pointed out above, manuscripts in Carolingian Europe used Lombardic and Uncial caps for initials and lead-in text blocks of the Carolingian minuscule that provided the model for our lower case. The cpas moved from a role of initials and emphasis into one of more general case (still effectively initials) over time.

But no country adopted the tricameral system of the old days as mandatory, this is the sad side of the story ;)

Since there's a smiley, this may be intended as a jest. But it wasn't clear from your post to me which tricameral system you meant - did you mean uppper and lower case and decorative initials?

While I think that small capitals ought to be recognized as a third case, I don't see a benefit of having any rule for always using a third case similar to the rules that require the use of capital letters.