I think having a one-time service for abandoned quests similar to the one-time item retrieval service could be very useful. For example, I'm trying to complete the Return to Ivalice raids, and on the very last quest, I accidentally abandoned it right as I was to finish it. Meaning I have to do the Orbonne Monastery all over again.
This might not be a huge issue if you play on a healthy Data Centre, but on Materia it's very, very hard to do Alliance raids other than Crystal Tower. The only reason I was able to clear Orbonne the first time was because I offered second chance points for folks on PF, and ran it unsynced. So now, I think I'm not gonna be able to finish this for a long time, which means I'm also barred from Bozja for the time being.
I'm sure there are other times where this service could come in handy.