This is a very well established idea. It's called dynamic quantization. Vary the quantization bit-width (or skip quantization altogether) on a layer by layer basis, using a calibration dataset.

EvoPress is the first time that comes to my mind, when I think of dynamic quantization.

https://arxiv.org/abs/2410.14649

This is a thing! For example, https://arxiv.org/abs/2511.06516