You have it correct. I would suggest leave it on during a day you are going to or are listening to music and turn it off at night to preserve tube life. If the electronic caps and such are already broken-in in the player then I don't see them requiring much time to reach their full potential.
Do you leave CD players with tube outputs on?
I was wondering how many owners of cd players with tube outputs leave their CD players on all the time. I have a Ayon CD-1 with a tube output stage. Based on input I received I've been turning off after listening and let it warm-up at least a half hour before each use. On the other hand, it is my understanding that the electronic circuits for CD players need around 72 hours of being on to reach their full potential. Is there any harm in leaving a CD player with tubes on all the time other than a shortening of tube life?