Have there even been any swearing in ceremonies since Dick and Babs?
No, because Dick's the only person for whom the oath was ever part of the story. It was more for him than anything Bruce needed. Jason, Tim and Damian never took one.
Stop here if you don't want to hear me complain about this version of Babs' story.
The reason Babs does it here is that in this retcon she's reduced to a young girl looking for validation from one male authority figure after another. Her vow here is really a ceremony to show that Babs has finally gotten what she wanted--unlike Dick's vow, which was the beginning of his journey, for Babs it's partly an end. There's no reason for Babs to have ever vowed anything to Bruce.