The problem with purely serious ones is just that they're a lot more difficult to pull off in the format that most webcomics follow. Good drama requires good pacing, but since number of pages directly correlates to amount of time the story gets released, what might be a well-paced story in a book where every page is released at once could be a much slower, potentially frustrating, experience on the web. This is why comics that focus on episodic content tend to do better than story-based comics.
Also, every individual entry in a webcomic could be somebody's first impression, so if somebody's first impression happens at the wrong time in a well-made story, they could be turned off. Imagine if the first Sherlock Holmes story you read, you started at Holmes putting his plan to catch the crook into action.
Side note: MS Paint Adventures gets around the first impression problem by having
http://mspaintadventures.com lead straight to the first page of the current arc, Homestuck.
I'd imagine the Superman serials were able to partially work around the problem of a day-to-day narrative by being able to say "It's about Superman", but most webcomics can't do that.
Story comics can and do work, it's just not as easy as doing a humor-based strip.