The view at CMOS is that there is no reason for two spaces after a period in published work. [...] So, in our efficient, modern world, I think there is no room for two spaces after a period.
The CMoS is hardly a final authority on the matter. It is just one common style, and is optimized for a particular presentation and publication style. It is also used by teachers to get students to write more words when their requirement is a page count.
