You know how Sansa looks up to Cersei as a god? So let's ask, what would Cersei do? Well, remember how Cersei planned to let the monsters fight each other - to great effect? That's what Sansa should do before playing this card, let Daenerys and Cersei duke it out and then press Jon's claim to mop up afterwards. Otherwise she just painted a big bullseye on Jon's back for both Cersei and Daenerys and you're risking a three way conflict where you hold the smallest force. Or maybe just let your beloved family member not be a king of anything just like he wants idk
Although I don't know why I'm saying any of this. In S8 GoT there's no negative consequences to doing anything really, strategy is non existent and the Stark girls are infallible.