Is it incorrect to use "and so" to link an antecedent and a consequent, when "so" alone would do it?
Note: there is an existing question with a similar title (Use of “ and so”) in the EL&U database, but it doesn't address the same issue. That question is about repeating some words from the antecedent. I'm asking about the appropriateness of "and so" itself.
The fact that it is fine to say "...and so do I," is because 'so' is used as an adverb. Or "...and so it goes." Both of these are 'so' meaning 'this way'. "I found a dollar, and so I picked it up," is using 'so' as a conjunction. It's the usage in this last example that I'm asking about.
I was late, and I got fired.
I was late, so I got fired.
I was late, and so I got fired.
I feel in my deepest soul of souls, or at least I kind of suspect, that this use of "and so" is technically incorrect, despite being incredibly common and almost no one having specifically asked this question until now. There are other questions regarding "and so," but not questioning whether this combination is itself proper. Did this come from spoken English, when someone says "and" to continue a story before realizing that "so" is more descriptive?
I can't think of another case of two coordinating conjunctions next to each other. Subordinating and coordinating, yes:
"I was late, and, because the boss saw me, I got fired." or even:
"I was late, and, so it wouldn't happen again, I got fired."
But these are different than my question.
A happened, and so B happened. Too many conjunctions!
Edit: This is not the same question as the suggested duplicate "Use of 'and so'", which I obviously saw before posting this, as I mentioned that I searched for duplicates before asking. That question was to a particular aspect of how to use "and so". I am asking if and why and how "and so" is justified at all. The other person did not ask whether "and so" is correct in itself.
The question marked as duplicate is, word for word:
If "and so" connects predicates such that the second is the result of the first, do we need to repeat the same words in the second?
My question is: Is it not in fact incorrect to use "and so"?