Oh, not that I mind; “I have greatly sinned” sounds just fine to my ears.I think you’re right there. But just like “to boldly go” or “to not care,” I think splitting the infinitive has become more accepted because the adverb is now seen as part of the verb. Thus splittting the verb such as “have greatly sinned” is not as taboo as it once might have been. But then neither are phrases such as “between you and I” and “who do you want.” English grammar is like no other because of the wordiness of the language, its ever-changing nature, and the quick acceptance of those changes. In other words, no grammar police.
However, I will never tolerate “between you and I” or “who do you want.”