If you could play Mystifying Song with other investigator, would you? It basically reads "get an extra round" in exchange for 3 resources - and as we know, time can be quite rare in this game (that's why we hate Ancient Evils so much).
But it is only Marie, the enfant terrible of the mystic class, who gets to perform this song - and for good reasons. The problem with Marie is there are just stronger mystics. To compensate your not-that-impressive stats, you are encouraged to practice the high risk high reward/huge fail playstyle, placing doom like crazy, abusing David for infinite money and signing Blood Pact for secure tests. Now the agenda is about to advance prematurely, you just lost 3 whole rounds and it is all your fault, your fellow investigators hate you - but wait! What's that sound?
Mystifying song is the insurance, answer to most what-ifs Marie naturally raises. Having it in hand allows you to play without restraint, at Marie's highest potential. Then Marie Lambeau is actually strong - and fun! The value of the other reward - whole extra round - obviously grows with more players at the table.
Mulligan or not mulligan away? The instinct says to drop it as the card does literally nothing for your setup. I dare say it's never that simple and you better think twice before voluntarily throwing away your insurance - and enabler.
The are also worth mentioning, because as much as commiting this card may look outrageous, sometimes the most valuable thing to do is to just pass a test.