Quite likely the first trope codifier for villains with sense of style is none other than the Bard himself, whose villains were oftentimes "gentlemen" dressed in the height of contemporary fashion. As Slobs Versus Snobs was, as always, entirely in effect back then, the audience of the Globe, comprised mostly of London commoners, found it easy to mock and dislike such a villain - long story short, putting the characters intended as despicable in fashionable clothing made them even more despicable.
This was completely reversed just a few decades later with Milton's Paradise Lost, the work single-handedly responsible for turning Satan from irredeemable villain to somewhat-likeable Anti-Hero, a case of Misaimed Fandom if there was ever any. Before Milton's poem, Satan was largely seen as corrupting, but dim-witted force whom everyone and their grandmother could beat in game of brains. Renaissance public, however, didn't see this as very threatening. Something better was needed and so Satan was revamped in accordance with Shakespeare's despicable villain rule - he became suave, charming bastard, mingling with aristocracy and outwitting the smartest minds. Milton, somewhat against his wishes, added finishing touch to this image and so Satan - the ultimate villain of the times - became Magnificent Bastard Anti-Hero with style, codifying the trope for centuries of villains to come.
Fueled by tropes like Aristocrats Are Evil (stemming from commoners' mistrust in their so-called betters), Sexy Villains, Chaste Heroes (as there were times where it just wasn't right for heroes to be sexy), the Man of Wealth and Taste flourished and even the waning of nobility hasn't seen it diminish. More even - with advent of giant, heartless corporations, he morphed a bit, to encompass not only aristocratic and stylish villains, but also those who prefer a nice suit to pimped-out coat. In those days, Man of Wealth and Taste is directly tied to both Aristocrats Are Evil and Corrupt Corporate Executive, pretty much ensuring its own survival.
