You are absolutely right. It would allow them to be practically identical to mainstream Christianity. Someone earlier on this thread started toward that argument from a JW perspective but it fell apart before even getting there.
As you are likely quite aware, the argument that I am presenting is not that there is anything wrong with the Passover having both pagan and human origins. Jews don't teach that. We acknowledge this truth and embrace our celebration wholeheartedly without excuse for how it began. There is no Devil that inspires pagans to worship him through false religion in Judaism, so adapting something from the Gentile world isn't necessarily wrong. Purim, for example, is celebrated using almost exclusively Gentile and pagan elements.
The idea that something has to be "sanctified" because it had origins in pagan society or because it came from a human tradition is a Christian way of dealing with the paradox they often create for themselves. Teaching that the world is under a curse due to Adam's sin and that the Devil is real and inspires paganism, they create a problem when they develop and engage in celebrations and observances that come from this "cursed world." They aren't breaking a real rule, but they are going contrary to their own when they do this.
The answer? You said it. "Jesus sanctifies!" Simple answer, no? They need to use Jesus as this type of answer because they tend to contradict themselves when they say "pagans are evil but we like their celebration elements that we adopt for ourselves." Thank God for the "Jesus-solution," then, huh? They reduce Jesus to a talisman almost by saying what is tantamount to "Jesus touched it so now it's good."
The reason that didn't even did start to work before here is that Jesus is not considered to be an answer to anything in my discussion. Remember, I'm Jewish. While I do believe and recognize that Jesus of Nazareth was a Jewish sage of the first century, I also recognize him as an imposter to messianic claims and dead...and probably long eaten away by worms. Whatever Jesus "touched" doesn't change the historical origins of anything.
Jews don't see the world as "cursed under sin due to Adam" or "under the control" of "the Devil." (As mentioned before we don't even believe in the Devil.) We see the world as innately good. Thus we have adapted practices from other cultures and attached new meanings to them, but we don't teach that such things were in some mire of evil that required Jesus to declare them "sanctified." And whatever new meanings we give these practices doesn't erase their origins.