While is common and understandable

While is common and understandable to think of the Preamble as merely a grand rhetorical “preview” of the Constitution, with no without meaningful effect, this is not entirely the case. The Preamble has been called the “Enacting Clause” or “Enabling Clause” of the Constitution, meaning that it confirms the American peoples’ freely agreed-to adoption of the Constitution—through the state ratification process—as the exclusive document conferring and defining the powers of government and the rights of citizens.
Source: ThoughtCo.

Should "While is common and understandable" be "While it is common and understandable"? It seems that "it" is not omittable to me. The version "while is..." seems to be infromal in American English. I am not very sure.

That is an error that is hard to understand. You are right. The word "it" has unaccountably been omitted. (Later in that same sentence "without" should have been omitted.)