You are also ignoring the obvious fact that Christianity went through some bloody and repressive phases, but reformed itself. Why can't Islam do the same?
Islam can't reform itself because Muhammad was not a holy man, whereas Jesus was. It is like trying to reform Charles Manson's cult.
Since I am not Christian, I can only speculate on your thesis. My understanding is that Jesus brought a new covenant of love and compassion to replace the old covenant of an eye for an eye etc.