I quickly looked through the list (1970s and 1980s) and the definition of 1HW must be very a specific chart listing thing because there are musician who have had who had careers independent of the hit. Chris de Burgh filled 2000 seat venues multiple times in my home city as part of multi city tours over 40 years. Philip Bailey, of Earth, Wind & Fire, and Phil Collins of Genesis and his solo career are hardly 1HW.
There may be true 1HW with no other music career success but you cannot tell from this list.