If you want to emit triangles to the rasterizer and you cannot stick to AMD hardware then you’ll need to render the geometry twice, once for the rasterizer and once for transform feedback.
If NVIDIA were going to follow (without a hardware upgrade), then ARB_transform_feedback3 wouldn’t have that restriction to begin with.
You can generally assume that core extensions are the shared subset of hardware functionality. So if AMD had to make an extension to get around an obvious spec deficiency, there’s a good chance that NVIDIA hardware simply can’t do it.