I doubt it would change anything but why shouldn't grand jurors be allowed to speak in a presumably, relatively free country. It adds openness, transparency, and legitimacy to the process.
What's the justification that it's so important that it overrides the persons first Amendment right?
Besides, the prosecutors released all the data. It clearly seems a legit shoot. Why can't they talk about it?
Here is one explanation:
Secrecy
Grand jury proceedings are secret. No judge is present; the proceedings are led by a prosecutor;[16] and the defendant has no right to present his case or (in many instances) to be informed of the proceedings at all. While court reporters usually transcribe the proceedings, the records are sealed. The case for such secrecy was unanimously upheld by the Burger Court in Douglas Oil Co. of Cal. v. Petrol Stops Northwest, 441 US 211 (1979).[17][18] The dissenting opinion was joined by Justices Burger and Stewart but concurred with the Court's opinion as to the importance and rationale of grand jury secrecy. Writing for the Court, Justice Powell found that "if preindictment proceedings were made public, many prospective witnesses would be hesitant to come forward voluntarily"; "witnesses who appeared before the grand jury would be less likely to testify fully and frankly"; and "there also would be the risk that those about to be indicted would flee, or would try to influence individual grand jurors". Further, "persons who are accused but exonerated by the grand jury [should] not be held up to public ridicule".[17]
United States v. Procter & Gamble Co., 356 US 677 (1958), permitted the disclosure of grand jury transcripts under certain restrictions: "a private party seeking to obtain grand jury transcripts must demonstrate that 'without the transcript a defense would be greatly prejudiced or that without reference to it an injustice would be done'" and must make its requests "with particularity".[17] Further, First Amendment protections generally permit the witnesses summoned by a grand jury to discuss their testimony, although Dennis v. United States, 384 US 855 (1966), found that such public discussion permits release of the transcripts of their actual testimony.[17]
The Jencks Act, 18 U.S.C. § 3500, requires the government to disclose to the defense any statements made by the accused to the grand jury, and, with respect to non-party witnesses, that after a witness has testified on direct examination at trial, any statement made to the grand jury by such witness be disclosed to the defense.
en.m.wikipedia.org/wiki/Grand_juries_in_the_United_States#Secrecy