Karen Silver and Philip Trauring, who writes the blog where Avivah Pinski found another claim against involuntary name changes (https://bloodandfrogs.com/2011/05/name-changes-at-ellis-island.html), make the same error, a logical error known as a hasty generalization. In both cases, what they prove is that someone has made a voluntary name change, but I doubt anyone has ever claimed that no voluntary name-changes occurred. Finding even a thousand such changes cannot disprove a claim about an involuntary name-change, so basing one's views on a single such case doesn't go very far.
Trauring's article notes the availability of "a book from the National Genealogical Society called Petitions for Name Changes in New York City 1848-1899 (on Amazon) which was published in 1984 and lists the name change petitions on file in the Hall of Records in New York City for the years 1848-1899." Note that this comes to 17-18 per year for what is now the Borough of Manhattan, and includes petitions for name changes from all applicants, and not just immigrants.
I went through legislation enacted from 1790-1940, looking for references to involuntary name-changes. I found none, neither positive, making such changes policy, nor negative, making them illegal. The first mention of name changes for people (legislation changing names for vessels and places is rather common) comes in 1867 when Congress, acting in its Constitutional capacity as the legislature for the District of Columbia, established a procedure for residents of the District to change their names, an issue elsewhere left to state legislatures; evidently, New York acted c.1848.
The other appearances of name-changes in legislation are in Section 6 of the Naturalization Act of 1906 and the Nationality Act of 1940, in both cases establishing a mechanism for voluntary name-changes at the time of naturalization that would produce documents. Without such documentation, a claim about a post-1906 voluntary name-change is on the same evidentiary basis as claims about involuntary changes, except there is reason why such documentation should exist. Given the number of petitions in Manhattan, don't hold your breath expecting to find documentation for a voluntary name-change after 1906 made possible by these acts.
The simple fact is that no-one knows where the "no involuntary name-changes" (NINC) notion comes from, including the historians at USCIS and those who claim it has been proven innumerable times. No-one can identify where to find an actual proof, and there are methodological reasons why such a proof cannot exist. In the absence of an actual proof, if you're serious about seeking the truth about your ancestors, you don't discard anything they tell you unless and until you have actual proof that what they told you is wrong. NINC appears to have originated to motivate the wholesale discarding of family narratives, which would destroy whatever data they include; it's conceptually not that different from burning down an archive.