There is a cap to how many immigrants can become citizens. Or are you talking about something else? The back log for immigrant->citizenship is on the order of at least 10 years currently unless you have money and influence to get it short-circuited.

The old "there's no clear line therefore there's no difference at all" trick.

Of course anyone can "become an American" (or in other words, the definition of American can be broadened to include anyone). That doesn't mean adding large numbers of new "Americans" each year (~1 million/year, for more than a decade now, even during Trump) won't change the character of the country, or increase conflict as different groups pursue their ethnic self-interest.