There are, of course, both advantages and disadvantages to an advertising-based business model. As you say, advertising is likely to be volatile during a downturn. Also, the type of sites which rely on the eyeballs--advertsing are often easy to 'spoof'. (Low attachment.)
The advantages of advertising is that it's simple to implement. For a YC-type company, with a few $K funding and a few people writing code, there is probably no easier way to start generating revenue. No sales team neccessary, no 'critical mass' of business customers, no need for corporate partnerships.
There are risks in any business model, succeeding will alwyas take incredible skill and incredible luck, but with $12 billion in advertising spending each year, many successful companies have been and will in the future be built upon advertising.