I used to use Postman but now I prefer to just build my own scripts in Python. I use the requests library and can setup things however I want.
But it takes seconds to get up and running with requests-html. And it can do anything Postman can do and more. I have no idea how people in organizations use postman though.
It's really handy for generating test suites to hand to people who don't necessarily have the skills to write Python / node / whatever code. Have worked at places where certain changes needed a Postman collection alongside for people to manually verify that it works.
(Also handy for un-coder people to make test suites, obvs.)
(Also handy as a quick-and-dirty "view this data via the API" when you don't yet have a web UI etc.)
For us, the fact that you end up writing "code" in postman meant it had a learning curve anyway, so it was a really short sighted win.
For everyone smart enough to write postman code, especially postman code that leverages the scripts and storing variables, a simple test project set up by a dev is going to be very worthwhile. Postman doesn't have a linter or compiler, and it doesn't enable easy viewing of changes in source control because it's just one big json file.