HDMI -> DP might be viable, since DP is 'simpler'.
Supporting HDMI means supporting a whole pile of bullshit, however - lots of handshakes. The 'HDMI splitters' that you can get on eg. Alibaba (which also defeat HDCP) are active, powered things, and tend to get a bit expensive for high resolution / refresh.
Steam Machine is already been closely inspected for price. Adding a fifty dollar dongle into the package is probably out of the question, especially a 'spec non-compliant' one.