They need to be willing, but it doesn’t say they get a choice or have preference for what they reincarnate as, or even if they know its reincarnate vs revivify or another spell
"You touch a dead humanoid or a piece of a dead humanoid. Provided that the creature has been dead no longer than 10 days, the spell forms a new adult body for it and then calls the soul to enter that body. If the target’s soul isn’t free or willing to do so, the spell fails.
The magic fashions a new body for the creature to inhabit, which likely causes the creature’s race to change. The GM rolls a d100 and consults the following table to determine what form the creature takes when restored to life, or the GM chooses a form."
They need to be willing, but it doesn’t say they get a choice or have preference for what they reincarnate as, or even if they know its reincarnate vs revivify or another spell
"You touch a dead humanoid or a piece of a dead humanoid. Provided that the creature has been dead no longer than 10 days, the spell forms a new adult body for it and then calls the soul to enter that body. If the target’s soul isn’t free or willing to do so, the spell fails.
The magic fashions a new body for the creature to inhabit, which likely causes the creature’s race to change. The GM rolls a d100 and consults the following table to determine what form the creature takes when restored to life, or the GM chooses a form."
Also, Revivify ? You dont get a choice in the matter. Hence, it would have made the joke work.