[jagaerglad]

I disagree (but also with the prestige theory) it's not really a thing in other countries with significant amounts of Persians such as Sweden or Germany, there the exonym is still more dominant and no-one tries to push "farsi" out of pride or anything.

I think it just was a random occurrence / perfect storm in the US where some Persian speakers moving there didn't know there was an English word for it, and where the local population were more used to hearing names of unknown languages, and it happened to stick around and start spreading. And _then_ it maybe became a cultural pride or whatever thing with media following suit like you said