A common sight in car boot sales and antique shops is the Zither Harp, an Autoharp without chord bars.
Clearly a lot of people bought them- whether anyone ever managed to get a tune out of one is less certain.
I should imagine that the less common instruments would tend to cling to the cultures of their origin, so German Americans would have been most likely to have a Zither, Spanish Americans the guitar etc.
It takes time to stir that melting pot.
Cheers
Dave