It seems to be that for SVG there are some special algorithms used to compute the overlapping curves in a special manner and the standard blender imported just can’t do this very good… if you search for SVG here on BA there where some threads about those problems… sometimes using other apps… sometimes separating some of the grouping in the SVG…
There are also the:
- Import Adobe Illustrator, PDF and SVG… and the
- Import SVG as curves…
addon… so maybe try one or the other…