To supplement the information in gpr's answer, I note a further feature of English texts of the 17th and 18th centuries: it was standard practice for printers to set place names and people's names in italics. Thus, the complete sentence that the poster cites, which is from Aurelian Cook, Titus Britannicus: An Essay of History Royal in the Life and Reign of His Late Sacred Majesty, Charles II (1685), actually looks like more like this:
His Restoration I can compare to nothing better than that easie, delicious, and jocund Temper of the Elements, of Heaven, the Air, and Sea, after a violent and outragious Tempest, or rather after the great Deluge of the World; at which Time, he prov'd himself the Noah's Dove, that finding no Rest any where, was receiv'd again into his own Ark, and brought a peaceable Olive-Leaf in his Mouth.
The italicization of which is somewhat unusual, and the italicization of Olive is rather mysterious as well; but the italicization of Noah is standard for the time. A quick scan of nearby paragraphs reveals that the words Seneca, Hercules, France, French, England, Cromwel, Rome, Janus, Muses, and Christendom are likewise set in italics.
It's easy to see how this additional level of distinction (between proper names and regular nouns) could lead to inconsistency. For example, Cook's printer italicizes Satyr—evidently the personification of satire—but not Goddess (referring to one of the muses). And though he italicizes Muses on one page, he sets it in regular roman two pages later. And why does he use italics for "the Great Chancellor" but not for "this Prince" three words earlier?
To some extent we inherited the proper name complication, as regular nouns became all lowercase, while proper names went from initial caps and italics to initial caps and roman. But I suspect that it's easier to keep track of which words you've initial-capped and which you've left lowercase than to track which words you've initial-capped and which you've initial-capped and italicized.
In any event, the downfall of initial-capped common nouns seems to have occurred at the same time as the demise of italicized initial-capped proper names.