Right and that is what doctrines are, which are the very same things that are heavily condemned by the Bible. They take a little bit here, take a little bit there, put it all together and thus abuse the very sacred Scriptures they think they are preserving. The Pharisees were heavily rebuked for such things. Apparently, it was such a big problem that even Peter of all people was saying it would get people destroyed. John said that altering his writings in Revelation would make someone lose their salvation.
This thing is is that the Scriptures already are the revelation from God and there is no invitation to add to them or take away from them. There is no invitation to take something Jesus, Paul, and anyone else said in what was recorded and mix it all together and form a conclusion other than the conclusion that was already presented.
As you said, there are no statements about the trinity in the Bible. With as something as important as who God is and the written testimony that Jesus revealed who God is then one would think that would be in the Bible, but of course it's not. Jesus was a strict monotheist and what we would call a Unitarian by today's standards. He plainly taught to worship, pray to, fast for, and serve the Father who he called the only true God. He lead by example and practiced what he preached.
For some reason, Jesus' teachings were offensive to a lot of people. It may not be readily apparent as to why, but when you love the truth it's difficult to assume the rationale of those who hate it. There is a major spiritual component to what God taught Jesus to teach about and it ultimately boils down to a matter a light versus darkness, not only in a figurative sense, but in a literal good versus evil sense. That's why they simply reject the matter of the Father being the only true God. The people are of this world are usually easier to reach than them as they have not been corrupted by their false doctrines.