Oddly, and this was true all throughout his career, Groucho was like a detached spectator who insinuates himself into the lives of those around him. This allowed him to provide a sort of existential running commentary of whatever the proceedings at hand, despite the fact that he was a causal factor of the chaotic circumstances and typically the loosely organized ringleader. It's as if his character was its own third person POV: enunciating the viewer's own thoughts amidst the anarchy while ever winking at the audience's prejudices towards class warfare and other sociopolitical insolences.
Ergo, the thinly veiled mean-spiritedness that so defined his characters is actually a mirror, but the audience is so busy laughing at themselves, they fail to recognize the conceit. Like Tyler Durden, Groucho is all the things we wish we could be, but are too insecure and/or frightened to openly admit to ourselves. Thus we create a surrogate copy of ourselves, or project one onto a willing host (such as Groucho) to embody these traits, even though all of these things are quietly, even desperately inside of us trying to break free.
Perhaps the reason it is palatable at all is because of the balance struck by the other brothers, particularly Harpo, who almost always represents the innocent and/or naive child needlessly suffering at the hands of the given film's antagonists.