Our faith rests on this one fact; Jesus' resurrection from the dead. So much so that even Paul acknowledged in 1 Corinthians 15:14 that "if Christ has not been raised, our preaching is useless and so is your faith".
So are we wasting our time?
I would argue that no we're not wasting our time.
John's gospel account of Jesus death is quite clear that when the Romans pierced Jesus' side blood and water flowed out. Anyone with a modicum of medical knowledge knows that in death blood and water separate. So we know that Jesus was dead. Also, he's been brutally attacked in his run up to the actual Crucifixion which would have helped to hasten his death.