There are some SEOs that do extraordinarily well for themselves. Think of an industry awash with cash, like say consumer finance. Does there exist an affiliate program in consumer finance? Does there exist advertising in consumer finance? If so, is there any space for a new entrant in this field? If yes, there exists at least a few SEOs who are probably doing pretty well for themselves.

There are many reasons why someone who is really good at SEO might not be rich. That goes for any white collar profession, like say lawyering. See that unrich lawyer, what's wrong with him? Maybe he's not good at lawyering, but is good at writing about lawyering or playing a lawyer on a social network, which describes quite a few SEO "experts." Maybe he's good at lawyering but not good at extracting value from it. Maybe he works in a sector where money does not naturally concentrate, like public interest law. Maybe he doesn't really care for money. Maybe he's rich and doesn't feel like talking about it. Maybe he's playing a different game or one with different time horizons.

As to whether you can make a full-time living doing SEO: yes. People do. Nota bene: most of the SEOs I know have diverse skill sets -- some understand broader marketing well, some have deeper technical abilities, some have ready access to capital, some have domain expertise or industry connections, etc etc. The field is quite like programming in that regard.