@CedricVidonne -- I'm not an expert in this, but I asked some colleagues...hope this helps!
After much trial and error, it seems that white space is only retained when the "responsive" check-box is ticked during Illustrator's SVG export.
There is no actual white space there, it really just depends on the application reading the SVG, in this case, Apple's Finder preview and AGSM. Unchecking the responsive box gives the result Cedric is trying to achieve when uploading. I haven't run into any responsive issues after testing this and viewing on multiple screens, so it should be an effective solution. Would love to see if there's any other alternatives.
Owen Evans
Lead Product Engineer | StoryMaps