“The bodies were intentionally left on display after death.” This was indeed apparently the case in other places, but not in Judaea, because of that law in Deuteronomy about burying people executed by hanging on the very same day after death.
But the rage of the Idumeans was not satiated by these slaughters; but they now betook themselves to the city, and plundered every house, and slew every one they met; and for the other multitude, they esteemed it needless to go on with killing them, but they sought for the high priests, and the generality went with the greatest zeal against them; and as soon as they caught them they slew them, and then standing upon their dead bodies, in way of jest, upbraided Ananus with his kindness to the people, and Jesus [son of Ananus] with his speech made to them from the wall. Nay, they proceeded to that degree of impiety, as to cast away their dead bodies without burial, although the Jews used to take so much care of the burial of men, that they took down those that were condemned and crucified, and buried them before the going down of the sun.
“The Jewish custom is to bury as soon as possible.” This is correct, Father, but there is also the so-called ‘secondary burial’, practiced by those who owned burial caves: when the flesh of the deceased - who was interred in a shelf or niche inside the tomb for the ‘primary burial’ - has completely rotted away and only the bones remain (usually in the space of a year), the bones were gathered and placed in an ossuary or bone box, which is then places somewhere inside the burial cave. (Obviously this custom is out of the question for trench graves.)
Jesus’ burial was a ‘primary burial’: His body was laid on a shelf inside the newly-hewn tomb. Had the Resurrection not occurred (thankfully it did), His bones would have been taken, put in a box and reburied in the tomb or (admittedly it’s a little ‘eh’ but not completely impossible) transported the bones to Nazareth or Capernaum if the family owned any burial cave there, since the Jews were traditionally big about being buried together with their relatives and their ancestors.