If your BBEG isn't a threat at a level where they have something to throw against Godzilla, they're probably not enough of a threat. The big, huge, final, ultimate battle of ultimate destiny is the time to pull out all the stops. And that means crazy stuff like this. Smackdowns are for the big stuff.
However, do keep in mind the limitations. There are either two or four rolls involved, here.
First, the summoning roll. Player burns edge to smackdown, sure. However, the spirit still throws dice to determine drain, as stated above. 12 dice, +6 for edge, with exploding 6's. Average of 6 off the initial roll, and another 1 and change off the explosions. Probably looking at something in the 6-8 range for successes. That's 12-16P drain.
Second, the player has to resist that drain. They probably won't die. If they're smart, they're going to have a sustained Increase Attribute spell on them from some source or another to give them +8 dice to drain. However, that is a serious wound. Going in like that is suicide, and that damage can only be healed by resting. However, come sunrise or sunset (read: not enough time to heal ANY of that drain), that spirit is gone. They can armchair it, send the spirit in with the team to do their cut of the work. They can go with the team despite the severe internal hemorrhaging and then die in short order leaving the spirit masterless. Or...
Third! They roll binding to actually have that spirit at their disposal for any appreciable amount of time. Spend three hundred drams, light enough incense to choke an elephant, and the spirit rolls double their force. In this case, the math makes more sense for the spirit to post-edge, so on average, we're looking at 24 dice, average of 8 successes, with 16 failures. Reroll. Average of 5-6 successes. Total of 13-15 ish. Which means...
Fourth! If we're talking 15 successes, we're talking about resisting 30P drain. That will kill your player on any natural roll, unless they are incredibly lucky and get many explosions spending edge. Not might. Will. And even if they somehow survive, they have a long, vulnerable recovery time ahead of them while waiting to besiege the BBEG. Which means the BBEG has time to make a move.
Realistically? If they're burning edge to summon this spirit, the most practical option is to burn edge on the drain so they're fresh for the fight, leaving them vulnerable to the dawn, should the BBEG have a good stall tactic handy.
Also, force 12? If this is the final game of the campaign... hasn't the mage initiated and boosted magic? I would expect 14 or 16.