"Pose as" means he pretends to be or acts as if he/she is what he/she isn't. This phrase is related to the noun pose: He stood in an unnatural pose. - Pose in this context means position which comes from the same Latin word. This can then be transferred to people taking a pose so someone can paint a picture or photograph them. Which in turn leads to creative poses, such as actors in costumes. Which in turn leads to sentences such as "He posed as an expert in drama." which could be stated this way: He took on a pose as an expert in drama. or He acted, or pretended to be, an expert in drama.
He poses a problem. means the same He presents a problem. There's no acting or pretending going on.
He poses a threat to me. means He presents a threat to me. Ditto.
The book posed a solution to a problem I had for a long time. means The book presented a solution to a problem I had for a long time. Once again, the book is not acting or posing.
If there is no pretending or acting going on in the sentence, there is no "as" after "pose".