For my money:

“To boldly go” conveys a state of boldness which almost incidentally takes the form of going

“To go boldly” conveys an action “going” possessed of a quality “boldness”

They are not the same. I need access to both. That’s all it takes.
Reposted from Adam Kotsko
The "to" is not a *part* of the infinitive, it's a convention for clarification since the infinitive takes the exact same form as most present-tense conjugations. The proof of this is auxiliary verbs (can, must, etc.). So there's nothing to split. The infinitive is just the verb, not "to + verb."

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