I think I remember seeing it back in the 90's, shipping Mothra with Godzilla almost as much as her with Battera. I think the original reason is because Godzilla is the male head of the franchise and Mothra started almost as early as the female head of the franchise. When two of your big 5 are more often protagonists, have been in the field for decades, male and female, and have legitimate personality, people tend to ship them, even if there's no legitimate reason they'd be together.
I do have a guilty pleasure love with the recent Mothzilla stuff though. Mainly because Legendary Godzilla/Mothra have the most reason for it and, again, it is cute