I think you are correct few start-ups and small businesses will ever incorporate and be taxed as a C-Corp. However, there are limitations to the S-Corps, such as a max of 100 shareholders and I think prohibitions foreign shareholders, so any public company is generally going to be C-Corp, the major exception I can think of are publicly traded banks who are N.A.s
C-corp taxes are subject to all sorts of rules. You can't do C-corp taxes on your own except in the most simple of circumstances. You definitely need a CPA (and a good one) if you're going this route.
An S-corp is restricted in the total number of shareholders, and the classes of stock. It also can't have retained earnings. That's it.
S-corps aren't really popular any longer. Everyone who might have benefited from an S-corp is choosing to form LLCs instead. Less paperwork. Less formality. More flexibility. It's essentially a partnership with the limited liability of a corporation.
Heck, even AOL was an LLC for a while.