As a proponent and builder of pointy, sharp-cornered and otherwise precariously angled guitars, I have seen and built many such instruments. Structurally, they're all perfectly "sound" (no pun intended), but sure, you DO have to take precautions against damage. You've never seen a BC Rich Beast? The top 2 points of the body are very thin and flat, almost knife-edged; the bottom 2 points nearly ALWAYS break off the 1st time you set it down too hard; and the upper points of the headstock are EXTREMELY fragile. As long as the wood itself is good and strong, you can get very close points and edges. The main drawback comes when applying finish: the sharper the edge, the more difficult it is to get a good thick layer of lacquer on it. The lacquer will tend to run away from the point or edge, so you will need to pay special attention to these areas. Because the finish will inevitably be thinner here than on the rest of the instrument, you also have to be careful when finish-sanding, so as not to go through it to lower layers or even wood. The "rounder " you can make a point or edge, the fewer problems you'll have.
More examples:
Viszikon
Firebird
Voulge