Going through the 5e Monster Manual I noted that the Erinyes had been added to the book again in their absence from the 4e MM. But they are described as being part of the regular infernal hierarchy, vying for promotion to higher forms. From what I can tell this clashes with what has been described in Fiendish Codex II back in 3.5e. So I did some research on what this was like in other editions.
In the AD&D Guide To Hell a mention is made of Asmodeus putting his daughter Glasya in charge of the Erinyes (p.46), but the entry of the Erinyes makes no mention of them being a group apart of the rest of Hell. In 4e there are a few sporadic mentions of the concept of promotion (The Plane Above, p.66) but the Erinyes themselves are rather different (MM II p.64-65) as more warlike beings with their seductive aspects being taken over somewhat by the Warder Devil (The Plane Above, p.139) and the Succubus (MM I, p.67). But then again, the Succubus swings all over the place over the course of editions from demon to devil to generic fiend (2nd/3rd, 4th and 5th edition respectively).
But what is the case for the Erinyes in 5e as of now? Looking closely at their rules (p.73) reveals that they lack the Devil's Sight ability that all other devils have and instead have Truesight, something that they share with the Planetar Angels, who are 1 Challenge Rating higher than the Erinyes. This is reinforced by their description (p.69) which says that according to legend they were once angels.
Are they for now regular devils and part of the hierarchy or are they still outside of the regular rank and file because of their status as former Celestials? I understand that a DM can invoke the Golden Rule and say whatever they want, but I'm curious as to what is the "normal" state of things.