Doesn't sound like you've been following the space. They exist, it's called LoRas. The Unsloth project is huge and whole purpose is to make it easy to train to train LLM LoRas. The reason you don't see LoRas on their own is because people who fine tune models merge them back into the base and ship the full model weights instead
Also see LoRAX, it's an inference engine that exactly does this, it can serve many LoRas off a single base model