The dirty not-so-secret of Attic Greek typography: it adopts the punctuation and capitalisation conventions of the European-language country it is printed in.
So names or adjectives of nationalities (Hellenic/hellenic, Hellene/hellene) will be capitalised based on where it is printed. The quotation marks will follow local practice (and there’s a special place in hell for whoever uses ‘ ’, which are so easy to confuse with breathing marks before capitals). Enthusiasm for exclamation points will depend on local practice, if not whim. (I remember being taken aback at a Dutch printing of the Iliad, chock a-block with “!”)
The one exception: proper names are always capitalised, because they are always capitalised in capitalising languages.
The semi exception: starts of sentences are often not capitalised, following mediaeval Latin practice. But you’ll see many editions where they are; and in Byzantine Greek, from memory, capitalised starts of sentences are normal.
So, do we need uppercase and lowercase in Attic? No. But then again, Attic at the time was quite happy with no space between words too. We use capitalisation in Attic Greek, because we treat it like the contemporary European languages we are used to.
Which raises the question: what would a country with a unicameral script do with Greek? How would India or Thailand or China print Greek?
… They’d learn Greek via some Western scholarly tradition or other, and they’d follow that particular Western tradition (or traditions). Sorry.