so any home game they give up comes at a loss of revenue. Rexburg arena is smaller than Marriott Center. So unless they charge a huge amount for tickets, they would be giving up revenue to sacrifice to have a game there. SE Idaho is known for frugality like much of Utah is, so not sure they would want to pay huge bucks for a regular season college bball game. Would the BYU-I admin be supportive of such a game? I would guess that BYU-I leadership would have at most mild interest in such an event, considering they are trying to deemphasize to their students the importance of watching sports in their life.
I could support a one off game in SE Idaho in the pursuit of growing a fan base, but I can also see the pursuit of such a game having a really low priority in things to worry about for BYU athletics leaders and coach Pope and staff.
You also mentioned BYU-Hawaii. Taking a regular season game to Hawaii would be expensive, certainly not cheap.