In the U.S., Rule of Professional Conduct 3.6 governs trial publicity, and while it is directly applicable only to lawyers, lawyers can't try to circumvent it through others and if others take actions that would violate the law it would cast doubt on the integrity of the lawyer. The rule says:
Rule 3.6. Trial Publicity
(a) A lawyer who is participating or has participated in the
investigation or litigation of a matter shall not make an
extrajudicial statement that the lawyer knows or reasonably should
know will be disseminated by means of public communication and will
have a substantial likelihood of materially prejudicing an
adjudicative proceeding in the matter.
(b) Notwithstanding paragraph (a) and Rule 3.8(f), a lawyer may state:
(1) the claim, offense or defense involved and, except when prohibited
by law, the identity of the persons involved;
(2) information contained in a public record;
(3) that an investigation of a matter is in progress;
(4) the scheduling or result of any step in litigation;
(5) a request for assistance in obtaining evidence and information
necessary thereto;
(6) a warning of danger concerning the behavior of a person involved,
when there is reason to believe that there exists the likelihood of
substantial harm to an individual or to the public interest; and
(7) in a criminal case, in addition to subparagraphs (1) through (6):
(i) the identity, residence, occupation and family status of the
accused;
(ii) if the accused has not been apprehended, information necessary to
aid in apprehension of that person;
(iii) the fact, time and place of arrest; and
(iv) the identity of investigating and arresting officers or agencies
and the length of the investigation.
(c) Notwithstanding paragraph (a) and Rule 3.8(f), a lawyer may make a
statement that a reasonable lawyer would believe is required to
protect a client from the substantial undue prejudicial effect of
recent publicity not initiated by the lawyer or the lawyer's client. A
statement made pursuant to this paragraph shall be limited to such
information as is necessary to mitigate the recent adverse publicity.
(d) No lawyer associated in a firm or government agency with a lawyer
subject to paragraph (a) shall make a statement prohibited by paragraph (a).
This isn't the only reason, but it is an important one. And, there are isolated circumstances, some alluded to in the rule, where a different approach is ethical and appropriate (e.g. to rebut improper public statements by others).