CD Player vs. music streaming

I studied the same question for a couple of years ,once the quality all in one players started to show up. I had the PS Audio Direct Stream DAC ( bought used) and the PS Audio Perfect Wave Transport. I wanted the convenience of not having to getup to change disc and maintain a 1800 cd collection, but not lose the quality of the playback. I purchased the Aurender N100 server with 2 TB storage HD and 120GB SSD for listening so no mechanical noise! The PS Audio DAC converts the files to DSD for Great sound quality. You will have to spend the time to rip all of your CDs to FLAC files, which in my case took me about a month and a half of 3-5 hour sessions every few days. Once it was done adding new files only takes a few minutes as you collection continues to grow.  The Aurender servers are turning up used here on Audiogon now frequently for almost half price. The money you save could help you upgrade your DAC if you choose. The PS Audio DAC gets an FREE update to improve the sound about every 6 months. It is also been highly praised buy the stereo reviews since it was introduced. I love the sound and with quality cabling and speakers you would be hard pressed to improve the sound with out spending thousands of dollars more. Hope this helps to solve your dilemma. Happy listening!!

I have recently gotten rid of my Ayre CD player because I finally found a music server and DAC that sound better IMO. I’ve gone with the dcs Bartók, along with Roon on a Roon Nucleus. 
The ripped CDs all sound better (again, to my ear) than they did on the Ayre CD player, plus convenience factor is great. I use Qobuz as a streaming service because to my ear their hi-res FLAC files sound distinctly better than the Tidal MQA files - not quite as good as the ripped CDs, but quite good enough. 

I’m really happy with the changeover, and the simplicity of one digital source and one analog source. 

When I had my SACD player and a Paradigm streamer (Tidal),  I would listen to both. When I got a Sony ES HDD player and ripped my collection to the drive,  I haven't listened to the CD player since.  

It has been proven over a decade ago that a cd will sound better played ripped from a hard drive than from a CD player. The most critical piece of the digital chain is the dac, and not all dac inputs are created equal.

Every music server you buy is a computer. The only difference a music server company will tell you is that it’s optimized for usb 2.0 playback whereas a normal pc/Mac doesn’t have that. Another gimmick trying to get usb to sound decent. There are dozens of other gimmicks/tweaks you can apply to usb to try to get it to sound decent.

If you like playing the silver discs, buy the best dac you can afford and use the i2s input on the dac if possible, coax if you don’t have a i2s input.
if starting from scratch, you can run Roon on a good performing server with 16 GB of ram and multiple cores and put this in a separate room never in the audio room. (I use a Mac either a Mac mini with 16G or an iMac with 24 G of ram, and neither of these computers ran over 20% of its processing power and just use Ethernet going out to the dac).
Get the best dac you can afford. I also use the PS Audio DS sr and DS jr dacs with their Ethernet connections. These dacs also provide i2s connections if your CD player has this output.
Keep it simple using the best gear.

Why complicate things by using a 3rd party music server by anyone? What happens if this 3rd party server crashes? How do you backup or more importantly restore your data when your disk fails? Do you know linux because that’s what most of these 3rd party music servers use (I used linux and Unix for decades in my work but this is not an OS for the computer/audiophile novice).
The music server people will tell you to use a nas which is fine but you will also need to back that up which requires another computer. I have swapped between different Mac computers depending on how I wanted to run things. I use an external drive for my data and my Roon backup and another external drive for my hourly backups. When I want to swap computers, I move the external disk with my data and Roon backup to the other Mac, point Roon to its backup, I restore Roon and a couple of minutes later, I’m back up and running. Try that with any 3rd party server

I found myself in a similar situation. I ended up buying an Audio Lab 6000 CDT Transport and use it with my Schiit Audio DAC.  I could not be happier. I almost spent more money on a CEC transport... so glad I did not do that!