Until the latter part of the 19th Century the children born abroad with U.S. citizen parents usually did not acquire U.S. citizenship at birth and had to naturalize after birth to acquire U.S. citizenship. This was during the early period when each State was responsible for establishing its own State citizenship and naturalization requirements. The Naturalization Acts of 1790, 1795, and 1802 attempted to address these problems, but they were repealed except for the one in 1802 left many such children without U.S. citizenship for decades to come. S, you certainly cannot use the word “always” to describe something that was usually not the case for many decades.
You are right, of course. But the feds recovered their power over the process after the Civil War. Until then Americans had dual citizenship, one in their state and one in the Union. The federal court system was far less extensive and accessible than those of the states. Most state courts regarded federal immigration laws somewhat like those of California do today’s immigration laws, more like guidelines than laws.