Can “positive news coverage” be considered a “thing of value” in a bribery case?
Yes. Note that a narrow, specific holding that "positive news coverage" is a thing of value is unnecessary because it is implied by the general notion of thing of value as reflected in US case law.
Several [U.S.] court opinions, such as U.S. v. Hernandez, 795 F.3d 1159, 1164-5 (2015), cite the following from the U.S. Sentencing Guidelines from year 2010:
Thing of value means anything of valuable consideration. For example, in a case involving the bartering of child pornographic material, the thing of value is the child pornographic material received in exchange for other child pornographic material bartered in consideration for the material received.
A subsequent version of the USSG incorporated the notion of "agreed [...] exchange [...] for the specific purpose of obtaining something of valuable consideration from that other person". See U.S. v. Hoppy, (U.S. Dist., M.D. Pennsylvania, Mar. 2018) (emphasis added).
Apropos of your remark ("My question is mainly focused on trying to understand how "thing of value" is defined in the US and other western democracies"), Mulhall v. Unite Here Local 355, 667 F.3d 1211, 1215 (2012) identifies what element renders something a "thing of value":
The Second Circuit commented on the scope of the phrase "thing of value" when it explained that "[v]alue is usually set by the desire to have the `thing' and depends upon the individual and the circumstances." United States v. Roth, 333 F.2d 450, 453 (2d Cir.1964) [...]. It recommended that common sense should inform determinations of whether an improper benefit has been conferred.
(quotation marks in original, emphasis added)
In the context of your question, Netanyahu's alleged offer to Elovitch reflects Netanhayu's desire to have the positive news coverage. That desire is precisely what gives that "positive news coverage" the status of thing of value, at least under the circumstances you describe. Consequently, in light of the Mulhall opinion, it seems inaccurate and unavailing for Netanyahu's government to portray as "impossible" that the positive news coverage be treated as thing of value in the alleged offer.
Additionally, see People v. Campos, 351 P.3d 553, 556 (2016) ("The primary purpose of obtaining employment is to receive the financial benefit of payment for labor performed"). It is clear that a politician's purpose of positive news coverage is to be elected for, appointed to, or remain in, public office. Thus, the motive for procuring positive news coverage [in exchange for lucrative regulatory concessions] easily translates to that politician's pursuit of a financial benefit that results from being in public office.
Netanyahu's alleged offer fits the meaning of quid pro quo, which in turn is material for a finding of bribery. U.S. v. Kemp, 500 F.3d 257, 281 (2007) reads:
The Supreme Court has explained, in interpreting the federal bribery and gratuity statute, 18 U.S.C. § 201, that bribery requires a quid pro quo, which includes an "intent
to influence' an official act orto be influenced' in an official act."
And the U.S. v.v Jennings, 160 F.3d 1006, 1014 (4th. Cir. 1998) reads:
The quid pro quo requirement is satisfied so long as the evidence shows a "course of conduct of favors and gifts flowing to a public official in exchange for a pattern of official actions favorable to the donor.
(internal quotation omitted)
Has it ever been prosecuted in the US before?
Briberies involving a thing of value have been prosecuted in the US, although there appear to be no rulings where the thing of value in a prosecution consisted of --or was explicitly said to consist of-- "positive news coverage".
That being said, it seems unclear and doubtful how the accused party(-ies) in your question could legitimately overcome the notions from US case law and construe the alleged consideration (i.e., the sought coverage) as "not a thing of value".