I need an Audio Detective

 I have worked in Audio stores for almost 50 years and only encountered a similar situation once.  Guy had bought a Fisher HiFi VHS machine and brought it back saying it didn’t work.  We hooked it up and it was fine. 2nd unit, same result.  I went to his apartment in Boston’s South End to see what was going on, and sure enough the thing had no output at all, plugged into the same amp input as his CD player, which played fine.  Cables were checked.  Finally occurred to me we were located a block from the Prudential Tower, where a lot of broadcast antennae are located.  I switched him up to an NEC deck, and all was well!  RFI was the culprit, and the NEC had effective shielding, where the Fisher didn’t.  This was after Fisher was bought by Sanyo, 

Whether gear sounds better left on or not is very much dependent on the gear. My Luxman sounds great even after a minimal warmup. My previous Class D amps needed 2-4 days to sound their best again.

If you don’t hear any benefit to leaving your DAC off, I don’t understand the problem. It may be worth trying a different AC circuit though, if that fixes your problem the noise is being transmitted through AC and a Furman with LiFT and SMP will fix you right up.

Try a few RF Chokes on the digital cables coming and going from the DAC.

https://www.amazon.com/rf-choke/s?k=rf+choke

So it's confirmed the DAC is emitting RFI garbage. I wonder if that RFI is permeating any other audio gear (besides the tuners) when it's ON, to the point it's having an effect on noise floors.