What usually happens is someone creates an API, one which did not initially have to handle much data, and then it just grew over time. (I guess it's similar to how a lot of the Internet's early application-layer protocols like HTTP, SMTP, etc. are text-based --- the text format was initially more "convenient" for a variety of reasons, but obviously is not very efficient at scale.)
Or, perhaps a more common scenario today, it was designed by people who simply had no knowledge of binary protocols or efficiency at all --- not too long ago I had to deal with an API which returned a binary file, but instead of simply sending the bytes directly, it decided to send a JSON object containing one array, whose elements were strings, and each string was... a hex digit. Instead of sending "Hello world" it would send '{"data":["4","8"," ","6","5"," ","6","C"," " ... '
Or, perhaps a more common scenario today, it was designed by people who simply had no knowledge of binary protocols or efficiency at all --- not too long ago I had to deal with an API which returned a binary file, but instead of simply sending the bytes directly, it decided to send a JSON object containing one array, whose elements were strings, and each string was... a hex digit. Instead of sending "Hello world" it would send '{"data":["4","8"," ","6","5"," ","6","C"," " ... '