I wouldn’t think a prescription for it until you get your skin issue addressed would be as much of a problem.
After all, these people already are obese, have dysfunctional immune systems, and have a currently untreatable and annoying skin condition.
If you can knock two of those out (which are 100% there), then the unlikely side effects you listed might be worth it.
“currently untreatable and annoying skin condition”
there’s nothing untreatable at all about atopic dermatitis ... there are numerous effective treatment medications, ranging from old and safe ones like hydroxychloroquine, which works in 33% of cases, all the way to brand new ones called JAK inhibitors ...