inflectional morphology - A Inquiry About Infinitive-To and Its Role As A Subordinator or An Auxiliary

If you're interested in grammar, as I am, I am sure you have delved into a thought process about infinitive to, and like me, you have probably questioned what it is, or what it could be defined as. My mind always wants to place it in the Eight Parts of Speech, and I know this is foolish of me to some regard, so I stray from it, but I still wish to designate it under something that can be explain it. So, this is the motivation for this post, this question: What is the infinitive to, and why?

Here are my thoughts: There are three real possibilities, going back through the times. First, we can say that it is part of the verb that comes after it (to go, to run, etc.). This could be supported by the claim that you are not supposed to "split" infinitives ("To boldly go"), but only that.

Secondly, we could consider it a subordinator. I came across this designation most recently in my studies of modern and transformational grammar. As of right now, it is still the one I accept, especially as a result of the trend of designating more phrases as clauses. It works, except it's weird. Do we call this a unique subordinator as a result of how it operates? For example, to-infinitive clauses call for non-finite verb forms, which typically have an implied subject as a part of their clause. For example, "I want to go to the store." In the infinitive clause, "I" is the implied subject, as a understand. So, again, this works. However, things get a little weird when other subordinators come into play. For example, "I'm excited for you to win the competition." Now, if I'm right, those of you will say that "for" is a preposition here, as a result of the new-grammar stuff, but I'm going to count it as a subordinator, as defined by my own beliefs and that of a lot of other grammars. So, how do the clauses work in such a sentence? According to transformational grammar, "for you to win the competition" is defined as an ordinary clause. So, does that mean that it also contains a secondary clause within itself (the infinitive clause part)? If so, how do those two clauses work in conjunction to each other when one is so integrated? "For you to win the competition" looks to just be one clause, but if that's the case, doesn't "to" have to represent something else?

This moves us on to the third way to look at things, which is to consider "to" as auxiliary verb, a defective one at that. There are a lot of things to support this, and it even allows for the split infinitive. Furthermore, it calls for a non-finite verb form to follow, like an auxiliary. But, as I said before, it's defective in the way that is all it can function as.

As I said, I still accept to as a subordinator, but I want to be proven wrong or right. Wrong by showing evidence of it being something else, or right by showing how clauses operate when it seems to be layered up.