It would in no way limit their power, in the manner that it was done. That is, they did not openly tell the public that they had either created the religion of that Jesus was their surrogate avatar. It was all done covertly and mostly targeted to a specific audience at first. In those days, the Romans traditionally welcomed the new practice of any religion that did not threaten them politically, or in some other manner.
In this regard fundamentalist Judaism of the day was indeed a threat, considering that ~10% of the empire was Judaic, and growing. To become a good Jew meant adopting all the 613 laws of Moses, which meant you had to withdraw from most Greco-Roman cultural practices. The Romans had, over time, attempted to make legal exemptions for the Jews to do so, but at the cost of growing social incohesivness if radical Judaism was to flourish. So the solution was to provide an alternative where the Jewish 'messiah' provides messages to his faithful that do not threaten Rome, but rather support it.
We have recently discussed here several new books, one which examines the teachings of Jesus in this manner and finds that indeed they all are messages that do not threaten Rome, in stark contrast to radical Judaism - which avidly supported the separatism of the Jewish holy land, the temple, and Jewish supremacy.
Of course, the notion of Jesus Christ as the Jewish messiah is hilarious from the Jewish perspective. Christians have long understood this and acknowledged this, but instead of realizing the true implications of this, they rationalized that this merely meant that (the Jewish) God had finally turned on the Jews for their constant misbehavior and infidelity to him. Ironically the Jews were typecast in their own holy book (the Word of God) as being rather morally suspect, starting out with their patriarch Judah fathering them via sex with his daughter-in-law, Tamar, whom he had mistaken for a street prostitute. She had to fool him into sex to gain her rightful inheritance priveledges. Well, no, before that he had sold his brother into slavery.