Please don't be so quick to jump to a conclusion of a "Roman creation." Eckhard Schnabel, in
Jesus in Jerusalem: The Last Days writes:
"This cry was not a self-curse but instead an acceptance of responsibility for the action of calling for Jesus’s crucifixion."
Catherine Hamilton, in
The Death of Jesus in Matthew: Innocent Blood and the End of Exile (pp. 28 et al.) relates that one of the themes running through Matthew is that of shedding innocent blood (Mt. 2.16-18; 23.34-39; 27.3-10, and here in 24-25). In her mind, the point is not that the people are asking to be blamed as much as Matthew is showing that they knew they were killing an innocent man.
Food for thought. Maybe it's not so "clear."