This is going to be the kind of “you’re giving them too much credit” explanation I normally dismiss, but I honestly think this is a thematic decision. Failure in Sekiro has a direct impact on the lives of others in your world. In the lore, when you die and resurrect (that is, every time you die), you are sapping the lifeforce of those around you through the use of the Divine Heir’s power, the consequences of which are manifested as Dragonrot. The more you fail, the more lifeforce you sap from the others in your world, the more Dragonrot spreads.
Spirit Emblems, according to the item description, “harbor the souls of the dead”, which is why you find them in the environment over the bodies of those who’ve been murdered, and why you sometimes get them from killing enemies. Every use expends a human soul. If you fail multiple times at a boss like Lady Butterfly or Genichiro, as I did, you pull tons of lifeforce from the people around you, sickening them, and expend hundreds of souls. Even careful, resourceful play expends souls, harms civilians. It’s a moral indictment of the inevitable collateral damage of war as much as it is a mechanical punishment.
That said, do I find it extremely frustrating to run out of spirit emblems at bosses? hell fuckin yes i do