Perhaps a useful addition would be new control lines on paths. What I envisage is that it would be possible to attach two lines (e.g. vertically) at either side of a shape. One end of each line would touch the shape and the other would point upwards. When I grab the control handle (using the node tool perhaps) at the top end of one of the control lines, all the nodes in the path would move horizontally in proportion to their distance from the moving line. This would allow the shape to be distorted. So simply by distorting towards an imagined vanishing point, it would be possible to get quite convincing 3d warping of any shape.
Being slightly more specific, the two control lines would form a pair, one of which is the invariant and the other the control line. The lines would initially be parallel and could point in any direction the user chooses (probably by moving the 'invariant' line). When the control line is moved, the all the points on the path move along normals to the invariant line. The distance they move is a linear function of their distance between the control line and the invariant line.
It would be necessary to be able to extend or shorten the control lines - they'd probably both extend or shorten together. However, this would be for practical reasons and wouldn't itself actually alter the shape in question.
To retain the ability to make further edits of the shape, it may be necessary to store the positions of the control lines in the document model (using Inkscape extensions because I don't think this could be represented in SVG). Obviously the SVG would show the distortion via the position of the shape's nodes.
I'd really like someone to implement this in Inkscape, although I'm afraid I'm not able to offer to do so myself.
Rick