I like the enthusiasm but no they actually work fine without positional encodings: https://arxiv.org/abs/2512.12167
But these days, there are many more options. They all maintain this positional information in one way or another. The one you cite (as I understand it) drops the positional encodings after pretraining, and keeps (e.g.) the causal mask.
I thought with NoPE schemes you don't even need it during pretraining
https://arxiv.org/abs/2305.19466
https://sebastianraschka.com/llm-architecture-gallery/nope/
Given the causal mask and the way attention works LLMs can implicitly propagate a signal for ordering