I put this idea on behalf of the end user.
I tried to get a sum of the area by Summarize Within tool like the attached picture, but the value is not what I expected because the Summarize Within tool uses “!shape.geodesicArea!”, while Shape_Area field is calculated by “geometry.getArea”. (Esri support told me this in the case 02269220)
My data is PCS (Projected coordinate system). Generally, the distance or area of the PCS data is calculated by "PLANAR", while these of GCS data is calculated by "GEODESIC".
To summarize the area or length for PCS data, the parameter for "PLANAR" is necessary !