And even observing the formal process of naturalization was spotty. A lot of people just moved here and never actually did it and nobody cared, they might not have even been aware they technically hadn't become US citizens.
My basic view on this is that historic norm was really the correct way to think about immigration and citizenship. If you move somewhere, howdy partner, nice to meet ya. If you stick around for a while, have a ballot, a flag, and we'll be glad to call you neighbor with all the rights of a citizen