The 14th Amendment should be interpreted to exclude children born to non-citizens because they are not subject to our jurisdiction.
Their parents are here illegally (in most cases), hence they are not afforded the rights of a U.S. Citizen.
Their parents are entitled to the process of applying for asylum or an adjustment in visa status, and depending on the result of those proceedings they may be able to acquire citizenship, but the simple act of a foriegn citizen giving birth on American soil should not automatically bestow citizenship on them or their children.