Because Sauron could disrupt them with arrows and Fellbeasts causing them to drop the ring somewhere in Mordor? Or because the eagles had their own agency and wouldn't be willing to perform such a dangerous mission while Sauron lived?
I'm not sure how either of those would apply.
If I remember well, enlisting eagles' help is actually discussed in books during the Council of Elrond. It's been years now and can't remember exact reasons.
Still, with resurection scrolls, a better example would be our heroes riding eagles all the time, and then thinking how they will cross the river, while the eagle is chilling beside them. Still, BG3 has so many contrivances, that that plothole didn't stand out to me.
