Gradients suffer from banding, both during editing and (more important) on PNG exports. The banding becomes apparent with gradients over narrow ranges.
I tried several ways to get from (Inkscape's) SVG to PNG and in the end found only one option that gets it right: Chromium. Source SVG and resulting PNGs attached.
There's a relevant bug report back from 2008: https://bugs.launchpad.net/inkscape/+bug/180693
Inkscape export (8bit per channel PNG):
Chromium, via clipboard (8bit per channel PNG):