Alan: the function does indeed write to a new file with blocksizes set appropriately.

Javier: the TIFF spec states that tile width (and this goes for height, I presume) must be a multiple of 16. Neither GDAL's GeoTIFF format page nor Rasterio docs make this clear. I'll add a note. I think that if you try 512 instead of 128, you'll have success.