I'm not even sure how to begin to respond to this post but I'll give it a shot. HDMI is all digital so if you let the digital audio pass through to the receiver or pre/pro there is absolutely no interaction or processing done on the audio signal from the PC side. If you're getting terrible audio via HDMI then whatever you have connected to it that is processing the signal is where the problem lies. I'm really not sure how using a USB DAC is going to be any better than using HDMI to a high end receiver or preamp/processor with quality DACs built-in. HDMI was specifically designed to transmit high end digital audio with no loss of signal or quality. USB was never designed for that purpose.
If you're only using your PC for audio playback then whatever "purist" configuration you're trying to use may work for you, but it's going to be a total PITA for most people. Many people have tried to suggest using a PC as a controller for a home theater system. Let's be very clear about one thing. A PC is a component in a system, not a controller. Trying to use it as a controller means you can't add other components because it has no input switching capabilities. All of the components in a home theater system are controlled by a preamp or receiver, including a Home Theater PC. Your way is nothing more than a kludged setup that offers next to nothing in the way of convenience or versatility. It's simply not going to cut it for the vast majority of users. You would never consider connecting a DVD player or other A/V component directly to a power amplifier so why would a HTPC be any different?
USB does have specifications for dealing with audio. Originally, the spec included USB Audio Class 1.0. This was limited to a stereo pair but it did support higher resolutions like 96 kHz / 24-bit. Not long after, the spec was updated to USB Audio Class 2.0. This supported multichannel high-resolution audio up to 192 kHz/ 24-bit. It has been supported on macOS and Linux for many years and is the preferred interface for a lot of audio interfaces used in recording studios. It took a while for Microsoft to finally support USB Audio Class 2.0 in Windows, which they started to do about a year or so ago. So, I wouldn't say USB was never intended for that purpose. You can use one of those 8 channel USB audio interfaces, which use very high-quality DACs, and they work pretty well in some home theater applications. Maybe not as convenient as an AVR but they will sound better than most AVRs priced under $3K. Those higher priced AVRs probably use similar DACs, like the ESS Sabre chips.
Just an aside... With my multichannel audio interface, I could play audio simultaneously through headphones and speakers. They have to do this for monitoring purposes. Using a software mixer utility, I could assign whatever channels I wanted to hear on the headphones (usually just FR, FL, and C). I haven't been able to find any AVR that does this. When you plug in headphones, the audio to the speakers is cut off. I'd like to do this again with an AVR because I have hearing loss. Instead of cranking up the sound and annoying the rest of my family, I'd like to plug in a pair of headphones. Of course, I'd need to have a separate volume control for the headphones.