As I recall, Roman citizens could have a quick death.
Crucifixion was not just for heavy crimes. Petty theft could earn crucifixion. If a slave killed his or her master, all the master's slaves (men, women and children) would be crucified,
Jesus was clearly not guilty of any heavy crime -- but then he was not crucified by the Romans.
We really don't know why Jesus was crucified. All we have are the gospel accounts, which contradict each other and go out of their way to blame "the Jews". John in particular is anti-Jewish, because the community in which it was composed had apparently been kicked out of the synagogue. The involvement of Pilate is really problematic. There are lots of things the evangelists couldn't have known: the discussion inside the Sanhedrin during the (illegal under Jewish Law) night trial--in John there is no trial, what Pilate and Jesus discussed in John after Jesus was taken inside the Praetorium (where the priests didn't follow because they wanted to eat Passover--although the three other gospels say Passover had already occurred--and Pilate specifically asks Jesus "Am I a Jew?", implying he's not), the report of Pilate's wife's dream in Matthew, which it is unlikely she made in public. The Gospels specifically say the Jews needed permission to execute Jesus (their preferred method was stoning, not crucifixion) because they needed Roman approval.
In John there is no "agony in the garden" and those who come to arrest Jesus "fall down before him". Clearly there are Jewish authorities present because the High Priest's servant loses his ear. As Paula Fredriksen says, the crowd howling for blood "comes from nowhere"--especially given what happened the Sunday before. It is highly unlikely that a person like Barabas as the gospels describe him would have been released (by a governor who had a reputation for brutality).
The gospel accounts disagree on the day (John vs. the others), the time (third hour in Mark, darkness from the sixth to the ninth hours; Pilate is still dithering at the sixth hour in John, and no darkness is noted). Only Luke has a "good thief", called an "evildoer" in Luke's Greek. In John the "two others" "crucified with him" say nothing, and nothing is said about them or their crimes--they are just "two others". In Matthew, both thieves (here called laestaes, "brigand", implying rebellion) berate Jesus. Mark also calls them "laestes" and they also both berate Jesus. John would never have Jesus say "My God, why have you foresaken me" and doesn't. John's Jesus needs no help with his cross, no Simon of Cyrene. John's Jesus looks after his mother (who has other children and doesn't need the attention really) and only says "I thirst" to "fulfill the scriptures" (and only in John are the brigands' legs broken but not Jesus's, whose side is pierced instead in order to "fulfill scripture"--the others say nothing about this). The others have no one near Jesus' cross, because the disciples are in hiding and only some Galilean women are watching from "afar off--"makrothen"). Matthew has a torn temple curtain, and earthquake, and resurrections when Jesus dies. No one else does.
Given all this, it is pretty clear that all the accounts have a heavy "PR" component, blaming Jews and exonerating Romans, John likening Jesus to the Pascal lamb on Passover, all stressing the foreordained sacrificial death of Jesus, and John stressing how calm and in control Jesus is. Each evangelist adds his own details to make the case for Jesus' innocence and conform to each evangelist's own religious views. (Jesus wasn't actually enthroned God and part of the Trinity until early in the fifth century or so.)
The crucifixion was a hard thing for Christians to explain--it isn't something that happens to ordinary criminals, it is something that Romans do to their enemies, so if it happens to your founder you need to come up with a reason. The gospels all try to exonerate the Romans, blame the Jews, and make Jesus an innocent man.
What really happened is speculation. A lot of people think that Palm Sunday worried the Romans--they always had troops in Jerusalem for Jewish "festivals" to nip any unrest in the bud. When Jesus overturns the money changers' tables in the temple (in John he had already done this some time before, and "the Jews" only decide to kill him (and Lazarus) after he raises the latter from the dead--Maurice Casey for one wrote a whole book claiming the Gospel of John is just not true but merely theology), the authorities are alarmed. The priests are responsible for keeping order, and under pressure from Pilate (giving Pilate some political cover) they arrest Jesus as a possible "laestes", and Jesus is crucified (for religious crimes he should be stoned under Jewish law). Thus, Christians had a Roman crucifixion to explain, and they tried hard to do so. Whether Jesus was actually a rebel or not, the Romans felt he acted like one and his following was very worrisome, so they got rid of him. The Jewish authorities for their part had every incentive to avoid a violent Roman police action against aroused inhabitants of Jerusalem.
Note that in his epistle to the Romans Paul urges obedience to the "authorities" ("all authority comes from God"). Jewish/Christian conflict in Rome had already lead Claudius to expel at least one synagogue from the city. Paul apostle to the Gentiles doesn't want to look anti-Roman.