What you are suggesting would have a HUGE cost per student. BYU already has one of the most extensive international internship and study abroad programs. But it's not that big. From t many BYU students they "can't afford" an international experience, or they don't want to leave their girlfriend/boyfriend/wife/husband.

I worked as a program coordinator for Japan internships and study abroad for 2.5 years after my internship in Tokyo. Japan internships were even paid, whereas none of the other international ones were, and it was still difficult to recruit students. Also the number of available spots has been declining rapidly for the last 20 years because companies don't see the value in bringing over a student to do minimal work for a very high price. My internship provided housing and a monthly stipend. Other countries have gone to unpaid internships for this reason, but most of the positions are with government or NGO's rather than for profit companies. That's not a huge pull for most BYU students who are looking for experience in their field rather than a "feel good experience."

In short, this would require a huge investment in resources (money, time, facility and staff) in addition to near impossible coordination with hundreds of other universities and companies to a level BYU doesn't currently come close to being able to do.

And you would have to have exceptions to the off campus experience for athletes, which opens up a can of worms that makes it impossible to require at all. Which leaves you with their current program, that while one of the better ones in the country, is still lacking for resources and opportunities for students, yet what we have is already underutilized.