The only thing I still use Postman for at work is when running API performance benchmarks, as I wasn't yet motivated enough to write a curl wrapper to do such tests and plot the results. Especially when doing things like ramp up etc. it becomes more than a simple for-loop.
Can someone recommend an existing command line tool for that?

Thank you, from a quick glance it seems to be able to do everything I need. I will try it for my next load test.