The issue is that a pen=0 does not mean zero thickness but a special thinnest that remains with the same width independently of a zoom level (in acrobat for example). The trick I used when I wasn’t able to get rid of a frame was to plot it fully transparent.
However, currently I it looks for me as this does not work for the frame of a colorbar (like for the frame of a basemap) as the transparency of the pen used for the frame also affects the transparency of the colorbar itself:
I don’t have a Illustrator anymore to confirm it, but I have the impression that the border line is already burned to the image and that is why we cannot separate the transparencies.