I'd venture out to say that we just don't hear about the smaller web-based businesses that make good money, because they aren't making millions or have millions of users (mainstream tech media only covers businesses like these). Similarly, a big VC deal is a sure way to get noticed.
So yes - I truly believe that is possible to build small, sustainable web-based businesses selling a digital product or service of sorts. And if you're clever about running your idea as a business, then there's no reason why you shouldn't be able to quit your day job in favour of working for yourself.