Firstly, I wouldn't call 'according to' an idiom; it's a standard way of introducing someone else's opinion, etc. In academic writing, I would say that it is OK to use idioms where appropriate, but this should generally be done sparingly. Idioms in an academic text to give it 'colour' or to show off the writer's command of English will look out of place. Of your examples, I think that 'about-face' could be used in, say, an essay on politics or history where a leader did one. However, 'all kidding aside' wouldn't have a place in an academic essay for me because academic writing should generally be serious and not kid the reader, besides which 'kid' is colloquial. If the idiom in not colloquial and there is a very good reason for using it, then use it. If not, then leave it out.
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