Well it makes sense in those terms, but you're filling a lot of gaps with material of your own which isn't in the text.

Also., you're omitting to mention that the gospels say that the Romans crucified Jesus because he claimed to be King of the Jews. Why would they do that if it was merely a favour for the Sadducees?

Also, John, possibly the most informed of the gospels, places the Temple cleansing incident at the start of Jesus's ministry, which is interesting.