Yeah they initially had chart success in the US - not quite the heady big #1 spots they had in the UK but success just the same - then the received a ban from playing there which lasted for several years to the end of the 60s. So their hits dried up and some of their most iconic songs just made no impact in the US. Davies seems to suggest though that some of these loved songs might not have been created without the ban.

“It made me root myself more in Europe, the folk tradition in Britain,” he told Tom.

"Perhaps, on the flip side, if that ban hadn’t been implemented, ‘Waterloo Sunset’ would never have been written."

Funnily enough from the late 70s through the 80s they seem to have had more success in the US than here. Though their songs were often covered by other UK artists.

https://www.newstalk.com/the-tom-dunne-show/kinks-frontman-ray-davies-on-his-bands-infamous-us-ban-700369