In the U.S., this is largely a matter of professional ethics applicable to attorneys. It is calculated to prevent a party from publicly disclosing evidence that would otherwise be inadmissible at trial in order to make it known to potential jurors who may decline to disclose that they have this information and could rule based upon it.
Every U.S. jurisdiction has ethical rules for attorneys that use the numbering system of the ABA Model Rules of Professional Conduct, and while they are not identical in every jurisdiction, the Model Rules are the foundation from which modifications are added by individual jurisdictions that wish to have a different substantive rule. This situation is governed by Model Rule of Professional Conduct 3.6 which states:
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), 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), 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).
In an extreme case, juror pool access to inadmissible evidence as a result of trial publicity could lead to a mistrial or a successful change of venue, and could give rise to contempt of court sanctions against a responsible party.
There are also other reasons not to disclose evidence in advance of trial that do not implicate this ethical rule from a strategic perspective that have to be evaluated tactically on a case by case basis.