When you turn on distorting linear gradients (Object > Envelope Distort > Envelope options: Distort Linear Gradients Fill), AI still won't do it when you use Warp Effects (Effect > Warp). This should be fixed.

I'd even extend this option to treat other gradients types, not only linear.

If you are able to easily make a gradient mesh using a gradient mesh tool, I would think it would be equally easy to unmake a gradient mesh back into a standard closed path instead of having to use Object > Offset Path and remove all values.