I did a German exchange in the 1970s and mine wasn't much fun either!
It was the first time our school had taken part in anything like that and they let the German school decide on who was matched with who. I had happily signed up thinking I would get to meet my German penpal, a girl about a year older than me. Well as it turned out the school in Germany decided that only their older pupils who were particularly good at English could take part so for the most part they were equivalent of VI Formers. However, we were an 11-16 school, German was a minority option and those taking part were all 13 to 15 years old, so big age and ability discrepancy for a start. Then to my dismay I discovered I had been paired with a boy! He was nearly 17 and I was barely 14. What the hell!
We really had nothing in common. I think he was probably very bored when he came to stay with us although my family organised days out at the weekends and school had other trips arranged in the week. When I went over there I was rather out of my depth. His family were actually very, very nice and horrified that I was so young. They had another son who was only 6 months younger than me and he was way too young to be considered for this trip, but actually we got on quite well and his English was about the same standard as my German so linguistically we might both of benefitted. As it was it did little for my spoken German as whenever I tried to speak to my exchange "pal" in German he just ignored it and spoke to me in English.
Golly I must have come across as a bit weird and awkward on that trip as I was so out of my depth.
Still, in principle I think they could be a good thing. I have known people who became great friends with their exchange families. Shame that the organisers made such a dog's breakfast of ours.
Edited to add- on the subject of mismatched exchanges reminds me of DHs tale of his French exchange. All the schools in his town took part with all the schools in their twinned town, so each school chose a school to be paired with. Because DHs school was the only Catholic boy's school in town the French school to twin with them was quite a prestigious boarding school with boys from all over, not just the local area. Also they were mostly from pretty well off families whereas the English boys generally were not. Apparently one of the English boys whose family lived in a council house was in an exchange with a boy who's family had a small chateau!