Introvert from an introvert family here. As a child, my parents never allowed me to go on a sleepover and we did not have overnight guests. I disliked languages and was convinced I was not good at them (teachers seemed to agree). I was sent on an exchange aged 13 despite having major reservations.
It was difficult at first (it was full immersion and I could hardly string a sentence) but things eventually clicked. I'm still friends with the host family, thirty years on. The language I learnt (and which I had every intention to drop the moment I could) went on to shape my personal and professional life.
The exchange helped me hugely with the language; it was all A* from that point. Living with strangers and having to understand what is going on in a real life situation is radically different from speaking over Zoom and watching movies, however useful those things can be language-wise. Quite aside from the language, the experience gave me extremely useful life skills. It really opened my mind and trained my resilience in a positive way (hugely helpful as a teen).
I now work at a university which offers all students the possibility of studying abroad. A short school exchange is quite different from a months-long experience but I am regularly amazed by how much the majority of those students who go to study abroad mature as a result and how the experience helps them to start (and then advance) their professional lives.
I am sending my DD on her first school exchange this spring.
Of course, there is no guarantee that things will always go right (and I know of people who hated it and asked to come back after two days) but I genuinely feel that in the vast majority of cases the benefits hugely outweight the potential downsides.