Not a myth. Perhaps a silly rule. But the infinitive in English is real, a verbal, that is, something formed from a verb, but which functions not as a verb.
I did not say the infinitive was not real. I said that the term "split
infinitive" is a myth because it's based on an incorrect definition of the infinitive. The infinitive is not "to go," it is just "go." It is often found without "to," in constructions such as "Can we go to the store?" or "She'll go ape when she hears this." It's a single word that often stands by itself. "To" is a marker that accompanies the bare infinitive in many formations; the two words together are called the full infinitive. You can split a full infinitive, but not a bare infinitive, because the infinitive, in its most basic, stripped-down form, is one word, not two. If it's okay for the "to" not to be used at all, then obviously it doesn't make sense to insist that the two words have
to be treated as a single indivisible word.
As I said, the "to" is analogous to the "have" in "have gone" -- a marker that's part of a certain grammatical inflection of a verb. There's no law that says you can't put words between "have" and "gone." "I have occasionally gone to that store" is perfectly valid; you don't need to say "I occasionally have gone to that store" or "I have gone occasionally to that store." Both of those are stilted and unnatural formations; it makes sense to put the adverb next to the verb it modifies. The helper word still plays the same role even when it's separated from the verb.
This is genuine English grammar; some of our verb forms are accompanied by a separate marker word that does not have to be immediately adjacent to the verb. The pretense -- the myth -- that the marker "to" must always be adjacent to the infinitive is a fiction based on a misapplication of Latin grammar rules to English. And it doesn't make sense in the context of English grammar and usage.