Why did the Romans use crosses for crucifixion?

Using crosses for crucifixions was about ensuring the public humiliation of the condemned and warning onlookers against engaging in certain behaviors. If Christ were impaled in a remote forest by the Romans and summarily buried, then other insurrectionists in Judea would not have had a sense of fear and trembling that would deter them from continuing in anti-government activities. It should be noted that in the Roman Empire, namely in Judea, crucifixions were generally used for insurrectionists e.g., Jesus Christ and revolutionary guerilla fighters e.g., Barabbas. The public nature of crucifixions and their exceptional cruelty were devised to strike fear into those who would commit crimes against the State.