Why a separate DAC?

DAC's are evolving quickly. I would say that if you can output your CD player to an external DAC, do so.
Two companies are my favorites, since they offer upgrades- Ayre and Schiit.
The latter offers the Gungnir and the Yggy, which I think compare nicely with the Ayre Codex. Both are relatively inexpensive. Under $2K used. 
Bob

As you obviously enjoy tube and analog sound, I'd recommend the Mhdt Labs Orchid R2R NOS DAC.  Cost $1100 sold through Linear Tube Audio.  I'd contact them and ask about their return policy to see if you can do an in-home demo.  I think your system will reveal significant differences between this and your Yamaha.  Here's a recent review on 6moons...

https://6moons.com/audioreview_articles/mhdtlab/

If you don't have a digital cable, I'd highly recommend starting with this one as it's very good and very cheap.  You'll need some burn-in time and pay attention to directional arrows. 

https://www.amazon.com/Geistnotes-Apogee-Wyde-Cable-WE-RR/dp/B01N29180M/ref=sr_1_1?crid=CE67OLG5CU63...

Best of luck in your digital journey. 

@gdrnBob I agree the DAC technology is changing quickly. I believe that I can use the Yamaha CD as output to DAC. @soix I really appreciate your advice on the try and buy. Thanks!

I am streaming TIDAL hard wired CAD6 from my modem in my family room to my Apple TV in the living room and have the Apple TV hardwired to my ARCAM AVR550.  I just found out I have not been even hearing 16 bit quality sound.  ARCAM makes a streamer that sells for $250.  Wonder if this can really play 16 bit and 24 bit.

I agree with the person who said he streams TIDAL.  Can't understand why anyone would spend the money on CD's anymore.  TIDAL is really so convenient.

DAC signal decoder may be an upgrade or may not. I recommend you choose a DAC signal decoder with multibit chip (sometimes called R2R) and a significant power supply, it is best to have no opamp in the audio sequence.
https://hdradio.vn/bo-giai-ma-dac/