Famous quotes all 'hop' to bigger names and end up getting stuck to the most famous person in a given category and period. It's a winner-take-all market.

Thus mid-19th-century American folk wit hops to Abraham Lincoln (who, for example, never said the thing about fooling some of the people all of the time), late 19th/early 20th American wit hops to Mark Twain (who never said the thing about the coldest winter being summer in San Francisco), mid-20th-century artist wisdom goes to Picasso (who never said great artists steal), mid-20th-century scientist wisdom ends up at Einstein, and so on. The celebrity names are large planets, whose gravity pulls in the small fry.

As past eras recede, more names get forgotten, so quotes get reassigned to the last ones standing, who therefore seem wittier and wittier over time. Churchill was a witty fellow but even he didn't come up with "if I were your husband I'd drink it" or "up with which I will not put".

Occasionally a celebrity attribution is correct, but the odds are surprisingly low, and if there's no textual evidence, forget it—it's a hopper.

It used to bug me that quotes always get misattributed, but it's a process of nature if you think about it. And there's a related phenomenon: they get optimized as countless people repeat them. Inelegant bits that are hard to remember or say out loud get dropped. An example is T.S. Eliot's "Immature poets imitate; mature poets steal" turning into "Good artists borrow; great artists steal", which is so much catchier. It's as if detaching from their origin frees them to evolve. Maybe the endgame is that they turn into pure proverbs and enter the language itself.

Edit: the internet has accelerated all this. It's easier for a misattribution to propagate—Google any famous quote and you'll see page after page of dreck—but it's also easier to search original sources as well as link to real citations (like Quote Investigator and Wikiquote). So both sides win.