I am not the best person to respond to this question, as my experience with fixies is limited to a single ride to the end of the block and back. And that was 35 years ago.

The only reason I can think of to tour on a fixie is to challenge oneself. But I find the kind of touring that I do is challenging enough -- even on a purpose-built touring bicycle.

Lugging 10 (or 20, 30, or more kg) up and down hills all day is something I don't mind doing on a tour; but only because my bike is designed to be comfortable and versatile under grueling conditions.