Steve, what means "HDMI is not hi-res"? HDMI 1.3 by its spec is a Dolby TrueHD / DTS-HD Master Audio bitstream compatible if devices support it. And even if we suggest that HDMI doesn't pass a bitstream hi-res signal, but using it instead of ATV's AirPlay with 16/44.1(-->48) is a huuuge difference, even for my non-perfect ears. And the signal is already PCM/88.2 on AV.
HDMI protocol was created for movies, not playback of digital audio formats. DTS is great for movies, but even DTS is nothing compared to 24/192 or 512DSD as an audio format. The other problem with HDMI is that lack of good DAC's and reclockers to reduce jitter. The best you can do to reduce jitter is the iFi SPDIF iPurifier which passes Dolby Digital/DTS. I use these in my Home Theater, but not good enough for my audio system.
If your HDMI sounds better than your audio system, you need to upgrade your audio system IMO.
Steve N.
Empirical Audio