You cannot analyze a sentence in a natural language — any natural language — by syntactic substitution and rearrangement, the way you are trying to do. Natural languages do not work that way. Your "3 => 4 => 5" is not even wrong.
You are also proceeding from an incorrect assumption: the phrase "The reason is because" is not redundant. It can be shortened to "The reason is" without changing the meaning, but that doesn't mean the word "because" is redundant! It is just playing a non-semantic role.
So it's not redundant, so what is it doing? First, think about spoken language. All spoken languages have filler words, which have no semantics but convey "I'm not done talking, I need a little more time to think of how to say the next thing." There are generic filler words, such as "uh" and "um", that can be used anywhere, but native speakers will often use words that fit grammatically and don't add any semantics, instead. If someone said "the reason is because X" out loud, the because would be a filler word in that sense. Again, it's not redundant, it's said for its effect on the conversation rather than on the communication.
Now, in written language there is no need for filler, but there is a notion of rhythm and flow, and English permits a fair amount of flex in sentence structure for the sake of rhythm and flow. Here are two examples (from the document linked in StoneyB's answer) where because improves the flow of the sentence:
“If the fellow who wrote it seems to know more of my goings and comings than he could without complicity of mine, the reason is because he is a lovely old boy and quite took possession of me while I was in Boston”
[1915, Robert Frost]
“… one of the reasons why I am not particularly well read today is because I have spent so large a part of the last twenty years rereading Dickens and Jane Austen.”
[1932, Alexander Woollcott]
Sentence flow is a highly subjective thing which you have to learn by osmosis. Don't worry about it until you are able to read fiction in English for pleasure without a dictionary. Then read a lot of fiction in many different styles, and your ear for it will begin to develop.