Palkia was almost always excluded from Legendary duties do to it being girlier than the others. When they offered to let it drive, it was so happy.
Giratina can't die, he's a Ghost. Anyway, Dialga can control time so he'll be able to predict accidents.
And then Palkia gives Dialga an Ice Cream Pizza and gives Giratina the Ghost Busters. Spazzy, foamy unconscious Dialga, a captured Giratina, and a Palkia that killed time because car crash and dead Dialga.