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When line and polygon feature classes are used as inputs in the Intersect tool, the tool outputs a multipoint feature class, instead of the expected point feature class.
This is by design. Lines intersecting with polygons may have multiple intersection points, which results in the multipoint feature class output of the Intersect tool.
To convert the multipoint feature class output of the Intersect tool to a point feature class, use the Multipart to Singlepart tool.