There are many phrases where both "in" and "into" may be used. For example, "Take that in / into consideration". In this example, "into" brings a stronger sense of specific and concrete action, whereas "in" is more often associated with a state. For "include into" however, the word "include" already has the sense of "put into", so using "into" sounds redundant. Therefore people don't use "include into" as much.

I can't think of a single context where we would ever say 'include into.'

I've never heard "include into" used.