To make clear when I say cloak I mean large and heavy outerwear that was between waist to floor length, fastened in the front, and often had a hood. I'm not so much thinking of the less expansive capes that continued to show in later decades.
The cloak and the cape verged between long and short throughout its history, from the tiny capes of the Italian blades worn on one shoulder during the renaissance, to the heavy riding cloaks of the more northern countries. But the long cloak really seems to have died out as a main fashion item from around 1910. By this time, the hood had long fallen out of fashion since it obscured the elaborate hairstyles which were so much in favour from the 18th century onwards. But collars could still get quite high, reaching its height around 1900.
The fashion for long cloaks was still popular with the very ornate garments of the Edwardian era. But even by that time, it was falling out of fashion, the easy-fitting oriental cocoon-coats and the heavy 'dusters' for driving became more and more popular.
The 1920s saw a fashionable take on the cloak with the mantle-cloak, and the 1930's saw another revival with some long cloaks for protecting the full-length evening dresses of the period. But the fashion was on the way out. Since then, the short shawl or stole has taken over completely, though the fashion for ethnic wear led to the adoption of the poncho, pareo, and pashmina in later decades, though these can't really be considered true cloaks.
And why did the codpiece, in the fashion of a double button flap, go out of style in favor of the single row clasps? It just seems like it would be so much more comfortable to have the wedding tackle in a sack rather than splitting the jewels.