I honestly have seen orthodox Christians, muslims, and protestants become Eastern Rite Catholics. They are just basically Orthodox Christians who agree with Catholic doctrines. I know they like some of the tradition, but there are reasons why Roman catholics dont do those traditions. Why not just be a Roman Catholic?
One reason is liturgy. Some people that have not been exposed to the Traditional Latin Mass but are disillusioned with the Novus Ordo prefer the much more reverent liturgies of the East.
A second reason is that they prefer the more mystical approach rather than the more reason based western scholasticism.
***A note of clarification: Eastern Catholics are in communion with Rome, otherwise they wouldn’t be Catholic.