Esoteric K-03 / K-01 Leave Power On ?

To each their own I guess. I have an Esoteric UX-3SE and I turn it off after I am done with it.. About an hour before I listen I turn it on. It does not draw a lot of power if you leave it on so again, it is all up to you. 

Since there is no on/off switch on the back I think the button on the front turns on and off all the circuitry.  They also don't have a spec for power consumption at idle.  The spec they do give is for power consumption of 27 watts for the K-03.   I don't think that amount of power consumption  would cause excessive heat or other problems even if that is the consumption at idle.  

I've never heard anyone say that their SACD player sounds better if they turn it off when not in use.  So I think if the blue light or the knowledge that your player is always on causes you concern, turn it off.  If that doesn't bother you and you think it sounds better after it's been on a while, leave it on.

I have an Esoteric UX-3 and I turn it on a half hour before I listen.  No need to leave it on all the time.

I have a Cary 306 SACD I’m using as a DAC. It has multiple power supplies internally and gets quite warm. In the summertime, I will turn it on a couple of hours before listening, and off when I turn in.
On Friday morning thru Sunday I usually have it on the whole time since I use it often when home. I tend to keep it powered up all winter, less heat and I’m inside more.As an EE in the computer field, It’s usually the current inrush that is most harmful to electronic components.  We recommended they stay powered up constantly for this reason.