A little late to this discussion, but I've taken a hard look at a few different intros for
the Cartoon Intro Cavalcade blog feature, and I don't think you're going to get the hard-and-fast rules that you're looking for. The best I can offer is the different factors I'd consider for why an intro sequence will name the show in the opening credits song and/or incorporate sound effects into it.
1.
What age group is the show aimed at? As Goldstar points out, saying the name of the show in the title sequence is going to happen a lot more often in shows aimed at younger audiences, especially educational programs where the audience may not be able to read yet. Shows for older audiences can assume more sophistication and omit the repetition of the name. I don't know what anime you're comparing against, but if it's aimed at the teen-to-adult audience, that might explain why their intro sequences look more like American prime-time live-action TV than other American animation (which is often aimed much younger, definitely true of most of the examples you listed above).
2.
Is the show named for the main character(s)? If it is, then I think it's more likely that you'll hear the name of the show in the intro sequence, because the song is going to be about the CHARACTER as much as it's about the SHOW (see
Curious George for a really good example of this).
3.
Is the title sequence trying to tell a story? Some intros try to tell a 1-minute story in their running time, to signal what the show is about and what to expect. Other times, intros are about "look and feel," intending only to introduce characters and locations rather than telling a coherent story. If the opening is trying to tell a story, I'd think you'd be LESS likely to hear the name of the show repeated in the title, but MORE likely to hear sound effects, because titles aren't useful storytelling devices but sound is. I don't think you can say much about either for look-and-feel titles, though. I'd say the overwhelming majority of anime I've watched are "look-and-feel" style openings, and that most of them choose to omit sound effects and naming the title, but that's more of a style choice.
4.
Does the show have continuity? This rule is a bit harder to quantify exactly, but my sense is that true serial fiction won't say the title or use sound effects. I'd say this consideration is really just a side-effect of some of the other stuff above -- real serial fiction assumes a more sophisticated audience and will save its heavy storytelling for the show rather than the intro.
Mix and match these different things and I think you get a good sense of when you'll hear the title in the theme song or if you can expect sound effects, although these are more like the Pirate Code in that they're more guidelines than actual rules. Looking at some shows in more depth:
Cowboy Bebop: This is the quintessential "look and feel" opening sequence to my eyes, also not named for anything exactly in the show and aimed at an older audience. Continuity is iffy -- most episodes can stand alone pretty well, but some definitely happen before others. This seems to fit all those rules above well, but I think it's the exception and not the rule.
G.I. Joe: A pre-teen to teen show (but younger than
Cowboy Bebop for sure), and the name of the show is the name of the team. Also a quintessential narrative opening credits sequence. No continuity in any meaningful way, so the opening serves as a way to introduce anyone and everyone to the show if it's the first time they're tuning in. All of the above nails why the name of the show is repeated as often as it is in the intro, and why there are sound effects all over it. Again, though, I think it's the exception in following most of the rules above.
Thundercats: I'd say elementary-school-to-pre-teen audience, so more likely to hear the title in the theme song. Also reinforced by the fact that the show is named for the main characters. I'd say it's not really a narrative, but they stuck in subtle sound effects to color the fight sequences a bit and add a bit of horror to Mumm-Ra's appearance. Don't think it had continuity, but it's already breaking a bunch of rules.
Doc McStuffins: Aimed at a younger audience and named for the title character, so expect the name in the song. Semi-narrative, so you do get some small sound effects. No continuity to speak of, which would also reinforce the repetition of the title in the intro. Follows more rules than it breaks, but it shows that some factors are more important than others (I think the age group explains why they say her name so often in the intro song better than any other reason).
Chuck and Friends: It's a pre-schooler show on the Hub that's named for its main character, but Chuck only says his name once in the opening credits song and it's not to say the title of the show. It's a "look and feel" opening, and matches the expectation that we don't get sound effects, though. No continuity, but that probably makes it more of an outlier if you start considering it. This show seems to break as many rules as it follows.
Yamato/Star Blazers: Aimed at older audiences in Japan and younger ones in the US, but both Japanese and English versions of the theme song say the title of the show. Also incorporates sound effects because they're both semi-narrative -- I'd say it straddles that category pretty evenly since neither old or new intro tells a coherent story from start-to-finish, but there are definite sequences and flow. Both shows were definitely serialized narratives, so the use of the title and the sound effects make it even more of an outlier.
Nerima Daikon Bros.: Definitely aimed at older audiences (with juvenile senses of humor, but that's a side point) and not narrative, but the theme song in English and Japanese both say the title (which is also the title of the band at the center of the show). Not a true serial, since it's a silly comedy, so I guess that's not much of a surprise. But again, it defies most expectations based on what you might expect by categorizing as I outlined above.
BTAS: The show that breaks nearly all the rules above. Aimed at the boys 6-11, but definitely also made for older audiences. Named for the title character and tells a story, but has no words and almost no sound effects (there's the bomb blast at the start, and I think you can hear a few more subtle ones; I'd even argue some of the musical cues are as good as sound effects). This one is exceptional because it doesn't seem to follow ANY of the rules, and yet I think it's one of the best intro sequences of any show ever. Which really underscores that the rules aren't rules at all, and breaking them can be as effective as following them.
The punch line of all this is that intro sequences are unique as fingerprints, and not all of them are intended to do the same thing. What you get in them is going to be highly dependent on the show itself and the creativity of its staff. I think it's fun to look at a credits sequence and see what it's trying to achieve (or I wouldn't have spilled all that digital ink on looking at a bunch of cool intro sequences). I would definitely suggest that this is a more worthwhile way to categorize and judge credits sequences than just on whether they say the name of the show or if there are sound effects. One size does not fit all.
