It's rather like trying to eliminate the Roman Empire by getting rid of Romulus and Remus...even if they did exist, wiping them from history doesn't erase the tens of thousands of people living on the Italian Peninsula in the 8th Century BC. The Roman Empire is still going to exist, it will just have a different foundation myth. Similarly, if Ishmael is wiped from the books Muhammad will still be around in the 7th Century as will the Arab peoples. Islam would simply be slightly different as regards its (alleged) origins.
Ishmael isn’t simply one person in the genealogy. He is the beginning of the genealogy. The Bible says that from Ishmael would come a great nation. If he didn’t exist the nation wouldn’t exist. Nation in the biblical sense being a “people” and not an actual country of course. Here is a biblical reference.
Genesis 17:20
And as for Ishmael, I have heard you: I will surely bless him; I will make him fruitful and will greatly increase his numbers. He will be the father of twelve rulers, and I will make him into a great nation.
I didn’t choose Ishmael/Hagar. I was just explaining why someone would. The Bible is clear that Ishmael was a wild man that was never at peace with his brothers.
BTW, the genealogy in the Bible is actually the most accurate of any ever recorded.
Here is an interesting link:
http://www.forumterrace.com/Questions/Historically.html