Sampling an implicit function on a grid shifts you to the world of voxel processing, which has its own strengths and weaknesses. Further processing is lossy (like with raster image processing), storage requirements go up, recovering sharp edges is harder...
But isn't this what the author is doing already? That's what I got from the video. SDF is sampled on a sparse grid (only cells that cross the level set 0) and then values are sampled by interpolating on the grid rather than full reevaluation.
