@Ross at Play
When I look at what is being done grammatically, I see a new phrasal verb being created. I think the verb boldly go has a different meaning to the verb go modified by the adverb boldly. While I've no objections to authors creating new phrasal verbs, I would not do so when existing words in their standard positions will suffice for the meaning I want.
Christ. Watching this forum talk about grammar is like watching the blind men trying to describe an elephant.
"To boldly go" is no more a "new phrasal verb" than "to go boldly" is. Both of them are an infinitive verb, "to go", modified by an adverb, "boldly". It's just that in one case the adverb has been placed after the verb, as is common, while in the other case, the adverb has been placed so that it splits the two parts of the infinitive. Thus, a split infinitive. That's what it is. That's the definition of a split infinitive. When people are all, "Danger Will Robinson! A split infinitive!" this is what they're talking about. When you start rambling about how it's really a "new phrasal verb", no one knows what you're talking about, including you.
And there's nothing wrong with splitting infinitives in English. It's mildly unusual but widely accepted usage, does not make a sentence syntactically invalid, and can sometimes change or clarify meaning, or just make a sentence sound better.
The reason some grammarians make a fuss about it is that the early formal study of English grammar used the formal grammatical rules of Latin, with which all educated men were expected to be familiar, as a framework for understanding, even in places where English As She Is Spoke really didn't conform well to the Latin model. The infinitive is one of those places. English infinitives work differently than Latin infinitives, not least in being two words rather than one.
Where in English the infinitive form of "go" is "to go", in Latin it's ire. And where in English there's no particular reason you can't drop "boldly" into the middle of "to go", in Latin jamming audacter into the middle of ire just doesn't work. So some excessively uptight grammarians decided that, because you can't do it in Latin, you shouldn't be allowed to do it in English, either — despite the fact that people had been doing it for centuries (the earliest documented instances come from Middle English, where the earliest documented instances of people claiming you can't do it are from the 19th century), and continued to do it where it felt natural to them even in the face of being yelled at by English teachers who took those uptight grammarians seriously.
And the reason "to boldly go" is preferable to "to go boldly" isn't anything to do with the meaning, whether denotational or connotational. It's because "to boldly go" is iambic, and "to go boldly" isn't, and iambic meter sounds better, and the phrase was originally written to be spoken dramatically for television.
And, yes, "sounds better" is a thing that's objectively qualifiable, if not quantifiable, and has long been studied. (There's a reason that Shakespeare wrote in iambic meter so much.) It's more important for poetry and script-writing than for prose, but that doesn't mean that it's not relevant for prose.
("Iambic" means that it alternates unstressed and stressed syllables: "to bold·ly go" vs. "to go bold·ly".)