Compress kodim.png to kodim03.dds (with no mips) to two BC7 modes (1+6):
Highest Quality Mode (uses Modes 1+6)
So the output .DDS file compressed to 7.69 bits/texel using miniz (stock non-optimal parsing Deflate, so a few percent worse vs. zopfli or 7za's Deflate). The RGB PSNR was 41.8 and the RGBA PSNR was 43 dB. It used mode 1 around half as much as mode 6.
Notice the pre-RDO compressed size is equal to the output's compressed size (7.69 bits/texel). There was no RDO, or anything in particular done to reduce the encoded output data's entropy. The output is mostly Huffman compressed because Deflate can't find many 3+ byte matches, so the output is quite close to 8 bits/texel. It's basically noise to Deflate or most other LZ's.