SAGA tool polygon self-intersection: time to prosess increases exponentially with increasing buffer width

With QGIS 3.10 I try to find overlapping areas and the number of overlaps of buffers with the SAGA tool "Polygon self-intersection". The tool works fine with round buffers around points with a buffer-width of five kilometers. When I tried to find the overlapping area with ten kilometer buffers around the same points the tool takes forever while qgis does not respond anymore. To approximate the problem I widened the buffer from five to six to seven kilometers and checked the processing time in the report. This was 6, 9 and 90 seconds respectively. So the wider the processing time increases exponentially.
To solve the problem I tried:

• to reduce the number of buffers, but there was no difference.
• buffers in Shape-File vs buffers in geopackage. But also no difference.

Can anyone confirm this behavior?
Unfortunately I also need the number of overlaps per overlapping area. So the tool is kind of perfect. Is there another Open Source alternative? So far I only know of the tool "find overlaps" in ArcGIS Pro.