I like what GEEEK have done with their cases, the designs look really nice and the prices are very low indeed. I would not be able to compete with these prices as I will be getting the parts laser cut by a third party, I imagine GEEEK will have their own laser cutters with large cutting beds.
Making parts out of a single sheet and bending them (if you have the equipment to do so accurately) is a very cost effective method as you reduce the amount of fixing parts/brackets/extrusions, etc, required to assemble the case.
Acrylic panels will always result in at least some flat edges, unless, as you sketched out above each edge had an angled/rounded profile joining the panels together. But that is where the extra cost comes in and will make the case expensive. For example a single 3D printed edge at a length of 200mm costs in the region of £10. Multiply that by 12 edges and the cost soon mounts up.
My initial cost estimations have been worked out based on production batches of 20 units. From my initial estimations based on quotations received from laser cutting companies, plus the 3D printed component costs, the front USB and I/O panel, nuts, bolts, screws, rubber feet and packaging, the total raw component cost is in the region of £80 - £90 (GBP Inc. VAT). Assembly and packing time will also need to be included and any other costs that may arise. This is where the target price of around £100 - £110 has been worked out from (plus shipping).
If the minimum production run was to increase to 50 units, the only components which would really see any benefit of scaling up production would be the Acrylic panels which are currently around 30% - 40% of the total component cost. So the price may reduce by around £10 or so if the demand was there.
But, if I was able to get this level of demand then I would probably consider investing in a laser cutter and try to bring the costs down that way. The laser cutter would need to be partially paid for through the initial case orders and so the price would likely remain the same as mentioned above. But, a benefit to the end user would be a variety of colour choices and design options could be made available as I would not be reliant so much on the economies of scale with ordering through a third party manufacturer. In other words each case could be customised with minimal cost increase.