He could well have existed. Some think he had an actual claim to the throne, which would have been a cause for concern for the Romans because he could launch a large rebellion, which in itself could have been enough to kill him.
The bible seems to be written to shift all blame from the Romans to the jews, which is ideal if its church is centred in Rome. Also, there is no way Romans are just going to become jews. Christianity then fills the gap, it offers the same things as 'pagan' religions before it, has a veneration for the sun, etc. Its written as to give sole power to the church of Rome through Peter, who then control all access to 'paradise'. The messages of love and forgiveness would be ideal for a nation that has brutalised so many and is about to be on the receiving end. They can send missionaries out with a new religion that preaches all of the things Rome didnt offer and hope it softens people who would like revenge.