For the glass to be the insulator we need, I'm assuming the author envisions a solid tube, with no airgaps (can't do fibre braid as that would allow gaps which means loss of insulation, or you'd need oil to fill the gaps.)
This means huge bend radius in the order of hundreds of meters. Not only that but laying it on the ocean bed would require trenching and full support to stop localised bending.
Now to the manufacture:
> The cable is then quenched in water to surface harden it, before it moves out of the back of the ship and falls to the ocean floor over a length of many kilometers (due to very low curve radius).
So that'll cause the tube to break. Glass builds up hige amounts of stresses when it cools down quickly (see prince ruperts drop) so needs an annealing step. ( https://en.wikipedia.org/wiki/Annealing_(glass) )
Moreover changes in temperature mean that using aluminum is probably going to cause the glass to shatter when the temperature changes. which means that you either need https://en.wikipedia.org/wiki/Kovar or somehow make expansion joints every n meters.
Finally that cable is going to be heavy, so unless you make it around the same densisty as salt water, it'll have so much weight it'll snap as soon as you try and dump it into the sea.
apart from that, looks good. well apart from the units are wrong to start with.
TLDR:
you'd need 5x the width of Polyethylene to achieve the same level of insulation at high voltages. but as silica tube doesn't bend and shatters really easily, cant be transported and has a slow extrusion rate, it seems logical to just use PE.