Actually there is a possible reason given in the answer you linked
*I'm unsure as to the reason why but I suspect that this is to give some protection to anyone receiving the copies from legal issues. If they didn't know they were classified then they have some defence if prosecuted.
I am not a lawyer and the issues here are quite complex but I found an article ( for fans for the movie it's an interesting read) which covers a lot of the background.
Essentially, although Ellsberg was (arguably) not stealing the information (as he was cleared to read it), disclosure of it to non-cleared parties was probably illegal,
But, if he removed the TOP SECRET indicator the receiving party could claim that they did not knowingly receive &/or publish classified information,
Whether the claim would be validated would be a matter for the courts and that opens up another can of worms for the government already affected by the leak.
...represented an unprecedented breach of the national classification system, and anyone in possession of it could face criminal charges, not only of stealing government property but perhaps espionage or, ultimately, treason. Indeed, that was the opinion reached by the Times’ long-time law firm, Lord Day & Lord. Senior partner Louis M. Loeb objected to the idea of publishing leaked military secrets in wartime, which he considered irresponsible and unpatriotic, and he warned that the government would be sure to prosecute the newspaper and its top executives.
The Pentagon Papers at 40
Eventually, of course, the general leak to many papers was eventually adjudicated as that the public had the right to know and that pretty much settled it