I think in addition to the solid points the three video essays made so far, I'd argue one reason there haven't been as recognizable of scores lately is because the opening music has gone from being an overture in the big epics of the 50s and 60s, to a title sequence in most other periods of film history, to a short blast under an opening crawl in the Star Wars films, to often simply being a short piece of music over the studio and production company logos.
That said, the Kelvin universe films have nicely contradicted that by featuring a strong theme for Kirk in the opening of all three films, and maintaining the same composer throughout, keeping the continuity there, though if the point of keeping the TOS theme until the end for the first two films was that they didn't really start their mission of exploration, then I kind of wish Beyond followed the teaser with the TOS score. If it was the 50th Anniversary, they could have even done a riff on the TOS opening and closing titles sequences, kind of like they wanted to do for DS9's "Trials and Tribbleations."
That said, the Kelvin universe films have nicely contradicted that by featuring a strong theme for Kirk in the opening of all three films, and maintaining the same composer throughout, keeping the continuity there, though if the point of keeping the TOS theme until the end for the first two films was that they didn't really start their mission of exploration, then I kind of wish Beyond followed the teaser with the TOS score. If it was the 50th Anniversary, they could have even done a riff on the TOS opening and closing titles sequences, kind of like they wanted to do for DS9's "Trials and Tribbleations."