"He went into bed" is not generally used. I suppose it would be possible in rare cases in which the subject had been ill for some time but not bedridden; and then the patient became worse and had to be placed in bed. " "He got into bed" does not imply that he moved from one location or status to another.
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ljswave2-He went into bed.It occurs to me that this could be two prepositions, "He went in to bed," where "in" refers to "into the bedroom," and thence to bed.