Says who, you? Maybe with a liberal, activist Supreme Court that could be how it's interpreted but the authors of the amendment made it clear illegal aliens would not qualify for automatic citizenship. So Congress is in their right to legislate through statute an end to the practice, then we can let this Supreme Court hear it.
Above is the first sentence of the 14 th amendment. That'a pretty clear language.
The best way to deal with the anchor baby problem is a new amendment.