Musilanguage hypothesis

There is a theory called the Musilanguage hypothesis that states that music and language first developed as one and then separated. Many critics oppose, but to my mind it makes sense in some aspects. Neanderthals may have started with what ever vocal productions they could make and then once they were distinguished as communication sounds and emotive sounds, language and music grew from there.
Let us look at a couple of different aspects of speech that relate to music:
Inflection/intonation: When most people speak, they fluctuate in pitch (unless they are monotone). The most common example in English is that we go up in pitch at the end of a sentence when we are asking a question, and down in pitch when we are saying a statement. This is also reflected in music as well.
Tone: Like they saying goes, "if doesn't matter what you say it's how you say it." Tone of voice can change a sentence from being serious to sarcastic, funny to stupid, etc. Emotion and dramatics could also be in this category and are definitely prominent in music and language.
Yet, there are some aspects of speech like semantics, pragmatics (things that differ beyond their literal meaning, for example: Do you have the time?), and syntax (grammatical rules) that do not have a direct relation to music. How did we acquire these if music and language were formed together? Perhaps that is the reason for their split.
Question: Do you think the Musilanguage hypothesis is valid? Why or why not?