Yes, but the issue is that they don't have identity. The idea of assigning unique identifiers to particles is doomed because, basically, "there are no particles

Yes, but the issue is that they don't have identity. The idea of assigning unique identifiers to particles is doomed because, basically, "there are no particles, there are only fields" (https://arxiv.org/abs/1204.4616 https://arxiv.org/abs/1204.4616). Particles are how quantized fields present themselves when probed by localized interactions. In general, they're also observer-dependent. The idea of assigning an "ID" to an object reflects a macro-level notion of re-identifiable objects persisting through time. But at the quantum level, that kind of classical individuality - object identity - doesn't exist.