Yes, a single DAC with multiple inputs can improve your current CD playback and streaming digital. For $1000, I would stick with a DAC, not a CD player with digital input. Reason is the DAC/digital input will likely be an after-thought on a sub $1000 CD player.
That said, I do own a nice CD player with multiple digital inputs. My Rega Saturn-R is an excellent CD transport/player and it has 5 digital inputs. But you can't yet buy one used for $1000. They are currently closer to $2000.
That said, I do own a nice CD player with multiple digital inputs. My Rega Saturn-R is an excellent CD transport/player and it has 5 digital inputs. But you can't yet buy one used for $1000. They are currently closer to $2000.