It seems you are trying to place points at regular interval along the line. To do so I'd suggest using:

point=arcpy.Point()

Outside your loop. Inside it use:

        theP=feat.positionAlongLine (i)
        point.X=theP.firstPoint.X
        point.Y=theP.firstPoint.Y
        pnt=arcpy.PointGeometry(point,SR)

and

points.append(pnt)

Don't forget to obtain spatial reference (SR here) from line feture class

It seems you are trying to place points at regular interval along the line. To do so I'd suggest using:

point=arcpy.Point()

Outside your loop. Inside it use:

        theP=feat.positionAlongLine (i)
        point.X=theP.firstPoint.X
        point.Y=theP.firstPoint.Y
        pnt=arcpy.PointGeometry(point,SR)

and

points.append((pnt,ID))

Don't forget to obtain spatial reference (SR here) from line feature class. The rest as per @WMrenn solution