casting a spell similar to Merlin's Interdict, a global enchantment, that saves the data that makes someone this person whenever a consciousness is terminated, and respawn it in a functional body

Maybe someone (the Peverell brothers) already did something like this, just incompletely. The data is saved... but not respawned; just collected somewhere. This may be what is referred to as "souls".

Of course, humans being what they are, even if some wizards notice the souls, they don't start thinking about reincarnating them.