Why use “formal” or “constitutional” instead of “on paper”?

Because “on paper” can unintentionally sound dismissive.

Consider:

“Emancipation gave Black Americans freedom on paper.”

A reader may understand this as:

“They weren't really free.”

That is not your argument if You mean:

The freedom was genuinely established as a matter of constitutional/legal status, but that legal change did not automatically transform society.

Therefore:

“Formal”

means:

existing as a matter of law or official legal status.

“Constitutional”

means:

established or protected through the Constitution.

These terms recognize that the legal transformation was real.

The Library of Congress confirms that the Thirteenth Amendment emancipated all U.S. slaves and describes the subsequent difficulty of creating a society in which formerly enslaved people could actually live as free people