LfP (https://learning-from-play.github.io/) was a work that inspired me a lot. They relabel a few hours of open-ended demonstrations (humans instructed to play with anything in the environment) with a lot of hindsight language descriptions, and show some degree of general capability acquired through this richer language. You can describe the same action with a lot of different descriptions, e.g. "pick up the leftmost object unless it is a cup" could also be relabeled as "pick up an apple".
That being said, the LfP paper stops short of testing whether we can improve robotics solely by only scaling language - a confounding factor and central to their narrative was the role of "open-ended play data". We do need some paired data to ground (language, robot-specific sensor/actuator modalities), but perhaps we can scale everything else with language only data.
Thanks to the pointer on the Andreas paper! This is indeed quite relevant to the spirit of what I'm arguing for, though I prefer the implementation realized by the Lu et al '21 paper.