This may be subjective, but are there any occurrences where a show in the middle of its run, changes its theme music (https://www.douxreviews.com/2020/06/five-best-and-worst-times-tv-shows-that.html), and the new theme is actually better?

The first one that comes to my mind is the original Magnum, P.I. with Tom Selleck. This is the original theme (https://magnum-mania.com/Forum/viewtopic.php?t=371&start=15) by Ian Freebairn-Smith (https://asmac.org/2018/04/16/master-class-with-ian-freebairn-smith/).

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It's very jazzy (https://i95rock.com/the-classic-rockmagnum-p-i-connection/), funky (https://www.reddit.com/r/unpopularopinion/comments/nk9qqm/the_original_magnum_pi_theme_song_is_better_than/), and all in all, decidedly '70s (https://magnum-mania.com/Forum/viewtopic.php?t=371) (bare in mind that the show would debut (https://www.primetimer.com/quickhits/the-original-magnum-p-i-premiered-40-years-ago-today) in late 1980). It simply wasn't as exciting (https://blog.teufelaudio.com/20-best-instrumental-tv-theme-songs/) nor did it suit the show's action like the later theme.

The more familiar theme (https://americansongwriter.com/top-8-tv-theme-songs-from-the-1980s/) that was composed by (https://www.cinemablend.com/television/retro-tv-theme-songs-that-still-slap) Mike Post (https://thecathoderaychoob.wordpress.com/2009/06/23/tuesday-is-theme-tunes-day-magnum-p-i/) and Pete Carpenter (https://thecreativelifeadventure.com/2022/09/16/friday-food-for-thought-september-16-2022/), wouldn't appear until about (https://www.hometheaterforum.com/community/threads/inside-mill-creeks-new-magnum-p-i-all-in-one-blu.375403/page-2) the 10th episode of Season 1:
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Happy Days- While Rock Around the Clock was a good theme, Happy Days are Here Again was better.

Growing Pains- A lot of fans didn't like the acapella theme that came in later seasons. But I really liked it.

Diagnosis Murder- Season 6 theme was tweaked adding a cool instrumental part.

"Walker, Texas Ranger" had an instrumental theme during its first season, but was later changed to "Eyes of the Ranger" sung by Chuck Norris which was better.

Family Ties original theme song was performed by Dennis Tufano and Mindy Sterling for the first 10 episodes. From episode 11 onward the song was performed by original recording artists Johnny Mathis and Deniece Williams, as producers were displeased with Tufano's and Sterling's version.

The Brady Bunch theme song was more memorable when it was performed by the kids starting in the second season.

IMO, the T.J. Hooker title track upgrade starting in Season 3 (1983-84), when the title was shown over footage of Hooker running into the gun warehouse (that footage from the climax scene of second-season episode "Lady In Blue"), and William Shatner got his "starring" credit on that same portion as well, was a far better theme music for that ABC/CBS action cop procedural than the one for the first and second seasons (early '82 and 1982-83).

The addition of The Professor and Mary Ann to the Gilligan's Island theme.

"The Partridge Family" changed its theme from "When We're Singin'" to "Come On Get Happy" in Season 2.

"I Dream Of Jeannie" also changed its instrumental theme in Season 2 to one that was catchier and easy to dance to. The theme in Season 1 was terrible.

"The Facts Of Life" had Charlotte Rae sing the theme in Season 1 and then wisely switched to Gloria Loring the next year.

"The Flintstones" used a slow and soothing instrumental in the first 2 seasons that was called "Rise And Shine". In Season 3, it changed to the more familiar and iconic "Meet The Flintstones".