Q:

Generating statistics from line and hex grid in ArcGIS Pro?

I have a process I use QGIS/mmqgis for.  I have a hex grid that I use for binning large data, and I have that hex grid overlaying a road network.  I use the "Join Attributes by Location (Summary)" tool to generate a new road network that has a series of statistics derived from all the cells a line traverses.  Maybe more helpful to see the principle:

QGIS will give me a new road network and each feature has a min, max, mean, sum, range, etc derived from all the hex cells that feature intersects.  In the example graphic, the processed top line would have a sum of 500 and the tributary line would have a sum of 495.
I have tried to reproduce this analysis in ArcGIS Pro for a series of users who only have Esri tools, and have not been able to do so.  I have tried using Summarize Within, and this "sort of" works, but it creates a duplicate of each feature (line) for each hex cell it traverses and thus gives me no statistics.  
How would I go about accomplishing this?  
Pythonic solutions are fine as long as there is an explanation of which method to use in particular.

A:

Input:

Workflow that will handle overlaps:
arcpy.Intersect_analysis("LINES #;POLYGONS #", "./intersect.shp")
arcpy.DeleteIdentical_management("intersect", "LINE_ID;PGON_ID")
arcpy.Statistics_analysis("intersect", "./intersect_Statistics", "W SUM", "LINE_ID")

Output:

