"
I get the impression that more Americans had personal phones way back when than in Britain."

Probably so. This country is so large, and communications were so hard in the 1800s and early 1900s, that every effort was made to build a system...and the first systems were designed BY Americans like Bell. We had 'general' access most places, and decent access in cities as part OF becoming 'of age' as a country.   

The transcontinental telegraph lines were already in place in the late 1800s, so phone lines could easily follow the same basic routes. (My father set poles and strung telegraph lines from the 1930s to the 1950s.)



I remember one time, as a small child, using a telephone similar to this. I 'think' it was at a rural farm in S.E. Kansas, where we were visiting one of my mother's old school friends.