There's always more to be said, but I have a past answer on this that I'll paste below:

For men, cloaks began to go out of fashion in the eighteenth century for everyday cold-weather wear, as they were replaced by the greatcoat. The greatcoat, originally associated with coachmen, was a loosely-cut garment that could fit over the ordinary coat (worn on an everyday basis, rather than for cold weather specifically - think of a suit coat), and had a collar and/or capelet or multiple capelets sewn to the neckline for further protection. It seems to have entered the fashionable world around the same time that English country dress was becoming something to mimic, in the late 1770s and 1780s. Silk or fine wool cloaks were sometimes worn by very wealthy men as part of ultra-formal "opera dress" through the nineteenth century, but eventually petered out. I know that they held on to some extent in military uniforms, but certainly don't know enough about that to go into detail.

Women had fashionably worn cloaks and capes of varying cuts throughout the eighteenth century, but sleeved outer garments worn on top of gowns (spencers, short jackets; pelisses, fitted long coats; witzchouras, fur-lined coats with hoods; etc.) were picked up in the 1790s, with plain wool cloaks being left to those who couldn't afford to follow new styles, or chose not to (as with Quakers and Shakers, for instance). Unlike the situation with men, mantles and cloaks had a resurgence in fashionable women's everyday dress by the early 1830s, as their very full sleeves (often supported from inside with whalebone or crinoline) could not be stuffed into a coat. This state of affairs fluctuated back and forth through the century as women's sleeves changed shape; when they were fitted to the arm, sleeved overgarments could be worn, and when they were full, as in the mid-1890s, capes were more normal. Throughout this time, women retained the formal opera or evening cloak, which is how capes continued to be worn in the early twentieth century when they were definitely seen as old-fashioned costumes otherwise - until the return of the fashionable cold-weather cape in the 1960s, but as with uniforms, that's generally out of my lane.

You may have noticed that I never answered "why" this happened, as you asked. The truth is, I'm not sure I believe there is a satisfying sociological explanation for this. Fashion is a consciously manipulated and somewhat arbitrary domain: every time something fades from prominence, there's a chance it will be gone for decades or centuries, and a chance that it will rebound in a cyclical manner.