If we were to apply this to the major doctrines of Christianity, they would be found to be false teachings...
Only to major false doctrines of Christianity. Of which there have been, and are many, from the beginning of Jesus Christ's resurrection from the dead.
Does the Doctrine of "The Rapture" ever include all of the other eleven verses in which the word harpazo is used?
You've missed the point entirely. Doctrine and prophecy of Scripture is not written in every verse, nor needs to be.
False teaching is only when certain verses applying to the same teaching and prophecy are excluded, in order to teach some verse or verses falsely out of context.
Does it ever explain that harpazo is just a verb that describes a simple action, like "stealing," grabbing a person and "forcefully taking them?" One biblical rapture resulted in Philip being taken only forty miles from where he baptized the eunuch.
Does the exclusion of these other "rapture" verses cause The Rapture Doctrine to be false?
Although you miss the point, you are trying to make a point, that appears to apply. However, who has ever mistaken Phillip's transportation by the Spirit from the Gazan desert road to Azotus, as though that were a rapture of the church?
It's called making an absurd point to unnecessarily complicate a good rule and teaching.
This should be the standard for all "doctrines." But, if it is done honestly and thoroughly, there would be more unity in the Body of Christ, and not so many semantic debates and doctrine wars...
False. Such divisions and heresies began when the apostles were writing doctrine and prophecy of Christ, and there were many.
And furthermore, this isn't just a good Bible rule for reading and teaching in context, but is the common standard of teaching and critiquing all books. It's basic literary comprehension 101. It begins in grade school, when the students are taught not to take things out of context, nor come up with something the author never intended to write.
Does any version of the Doctrine of the Trinity include the verses used by non-trinitarians who want to prove "the Father and I are one?" (Other than falsely stating that "one" means unified/in unity )
Oh well, now we see the main objection: The rule also destroys a major false doctrine among some Christians, called 'Oneness'. I.e. the Father is the Son is the Spirit, and the Spirit is the Son is the Father, where all the Godhead is the same one Person.
Which of course separates John 10:30
"The Father and I are one", from John 17:11 & 22, where Jesus prays the Father, that His people be made one, even as They
are one.
Jhn 17:11
Holy Father, keep through thine own name those whom thou hast given me, that they may be one, as we are.
Jhn 17:22
And the glory which thou gavest me I have given them; that they may be one, even as we are one:
We see how Christ in Scripture always gives verses to prove or disprove any doctrine taught by man, whether it be from all the applicable Scriptures of God, vs the errors of man separating certain Scriptures from others, that pertain to the same thing: The Godhead unity of Father, Son, and Holy Ghost.
It's impossible for the Father and Son to be the same one person, when all the sons of God in Christ Jesus are made to be one, even as the Father and Son are one: Which would make all the sons one person, not many members of the body of Christ, but only the same one member.
If we apply this concept only to the "doctrines" that we don't agree with, and not allow for others to apply it to our pet doctrines, then we're heaping a helping of Judgement on ourselves.
It's those not applying this standard literary rule, that change all manner of writings and books, that they don't agree with, into something different than the author intended and wrote.
Such as Oneness teachers separating certain Scripture on unity of the godhead from other Scriptures isolated out of context:
The Father and I are one, is in itself commonly understood as unity, since the Son on earth could not also be the Father in heaven. Nor does he simply say,
I am the Father. Or,
I am the Son and the Father.
Even the ones falsely accusing Jesus of blasphemy for calling Himself the Son of God, understood He was making Himself
equal to God, not saying that He was the Father from heaven:
Jhn 5:18
Therefore the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God.
So your object confesses your own major error is one of those destroyed by taking all Scriptures together in context, that pertain to the Godhead of Father, Son, and Holy Ghost.