I think I've seen a rather pragmatic hack that has been used in Google Earth for their stitching of terrain: They simply add a kind of skirt at the boundary of each square chunk [0], so that there aren't any white/black pixels. There may be some artifacts between LoDs but they soon disappear when the next chunk gets more refined.

Edit: I think the Google terrain skirts were slanted, rather than falling straight down, so two neighbouring skirts intersect in a V.

[0] https://www.researchgate.net/figure/A-terrain-chunk-a-withou...