The shelf the LP12 sits on looks very rigid to me. If it runs the full width of the unit, the ends are trapped making it far more rigid than if where sat on cones. If the shelf is attached to the vertical pieces of wood either side of the LP12, it is effectively being help up.
With regards the Vulcan being lightweight, the wooden shelf isn’t that light, a piece of arolam would be much lighter. Plus if lightness is the reason it sounds OK, why do people go to the expense of putting a piece of heavy glass on top of the wooden shelf.
Regarding the rigidity, I don't think it's great that the shelf is supported outside the feet of the LP12 - I would expect some deflection with this design. On the original Audiotech, with the original LP12 feet, it goes on a straight line onto the spikes in essence. This means the shelf doesn't deflect. With the current setup I wouldn't expect it to behave the same.
The choice of material for the Vulkan shelf at those dimensions is actually quite light and rigid at a reasonable cost. You could probably reduce the weight, but can you do it at the same cost while keeping it rigid?
Lastly, re: glass, people have done all sorts of things to LP12s that don't necessarily make that much sense: glass, granite, sorbothane feet, clamps... Whatever floats their boat, but there is a reason the recommendation is for light and rigid. ;-)