Some BC7 format references:
Source to CPU and shader BC7 (and other format) encoders/decoders:
Khronos texture format references, including BC6H and BC7:
It may be possible to add ETC1-style subblocks into a universal GPU texture format, in a way that can be compressed efficiently and still converted on the fly to DXT1. Converting full ETC1 (with subblocks and per-subblock base colors) directly to BC7 at high quality looks easy because of BC7's partition table support. BC7 tables 0 and 13 (in 2 subset mode) perfectly match the ETC1 subblock orientations.
Any DX11 class or better GPU supports BC7, so on these GPU's the preferred output format can be BC7. DXT1 can be viewed as a legacy lower quality fallback for older GPU's.
Also, I limited the per-block (or per-subblock) base colors to 5:5:5 to simplify the experiments in my previous posts. Maybe storing 5:5:5 (for ETC1/DXT1) with 1-3 bit per-component deltas could improve the output for BC7/ASTC.
Also, one idea for alpha channel support in a universal GPU format: Store a 2nd ETC1 texture, containing the alpha channel. There's nothing to do when converting to ETC1, because using two ETC1 textures for color+alpha is a common pattern. (And, this eats two samplers, which sucks.)
When converting to DXT5's alpha block (DXT5A blocks - and yes I know there are BCx format equivalents but I'm using crnlib terms here), just use another ETC1 block color/intensity selector index to DXT5A mapping table. This table will be optimized for grayscale conversion. BC7 has very flexible alpha support so it should be a straightforward conversion.
The final thing to figure out is ASTC, but OMG that format looks daunting. Reminds me of MPEG/JPEG specs.