I had initially had trouble setting an assignment to accept all filetypes using the Python canvasapi, and decided to try to the Live API. I tried leaving the field blank on the live API, and it didn't work. It appears to only send data from fields that are not blank. I tried empty quotes ("" and ''), brackets and braces ([], {}), the word None... nothing works.
You're right that Postman is better overall. I just like the documentation and quick boxes of the live one. Here may be a case where the live API cannot do what I want it to. Thanks for the suggestions @jerry_nguyen . Using POST with allowed_extensions=[] ought to work.
I did figure out how to do it with the Python canvasapi, something like
assignment.edit(assignment={'allowed_extensions':''}
.