Boutique DACs don't support HDMI usually because then they'd have to actually compete on equal footing with AVRs, which already are basically HDMI DACs. To offer some kind of comparable value, vs a few hundred dollar 5.1 AVR, that also includes an HDMI switch, processing, remote, bass management, movie codecs.
Simply put, DACs are snake oil. You cannot tell in a double blind study the difference between one DAC and another, and the DACs in most cheap AVRs already far surpass the threshold of human audibility. Trying to improve on sound quality by upgrading your DAC is basically a foolish way to go about it, because any audible differences will be elsewhere in your system. Probably the speakers themselves. Or the source recordings. Or room treatments. None of which have any relevance to increasing from, say, a 24 / 96 DAC with 110-114 Db Snr in a typical AVR to a higher end one. 2 channel DACs are the royallest of the royal rip offs in the "audiophile" world. A commodity DAC should be about 1$, that's it. Beyond that you cannot tell the difference. This is old, old tech, and the only benefit to upgrading is in the codecs or processing that is added. Which means getting an AVR because most DACs have ironically minimalist processing which means they are basically worth about 1$ in terms of sound quality.