One daughter took a semester abroad in high school. We also hosted two different international students at our house during high school (one of which was from the family that our daughter had stayed with). Your list of Pro’s and Con’s looks accurate to me. However, IMHO the pro’s have vastly exceeded the con’s in importance (at least in our experience). For us this was a very strongly positive experience.
Our daughter when she was abroad studied entirely in Spanish. She returned essentially bilingual. She gained a much better understanding of a different culture. She was on pass/fail while she was abroad, but the comments from the teachers abroad made it look like she would have had straight A’s if she had gotten grades (which would not have changed her overall GPA in any meaningful way). She had a very interesting experience. I think that she also returned home with a greater confidence in herself. I think that this confidence helped significantly when she went off to university a couple of years later.
The missed activities at her school was offset by more activities at the school she was attending abroad. She made more friends (and still occasionally communicates with her friends from abroad). The math and science overseas was probably not as rigorous, but she gained strength in her Spanish and in the history and geography of South America. She ended up as a science major in university and started university with great grades in her science classes, implying that she still was well prepared.
I do not think that the semester abroad had any meaningful impact on university admissions. If anything it might have helped a little bit, but I do not think that it changed any outcome.
For us the study abroad was arranged through her high school. The only additional expense was the airplane flight to get there and back. Yes this was an additional expense but IMHO was very much worth it. In both cases where we hosted students the parents of the students that stayed with us offered to reimburse us for any expenses that we might have needed to pay for. We refused largely on the basis that it was such a joy to host their child for a couple of months.
I think that it is worth doing in either high school or university or both.
However, this is IMHO not a good choice for every student. I do not actually know how to predict which students will enjoy and do well during a study abroad.