Not quite what you're asking but.....I've got a Yamaha amp with a dedicated dock connector on it for Apple devices. I can chuck an old Iphone with ALAC files on it into the dock (which I acquired for ten bucks) and it sounds bloody great. Don't think I'll be needing the $20K CD player any time soon
But that doesn't use the 3.5 mm output, or, as I remember them, the "stereo mini". The headphone output is analog, and runs through the phone's amp, as well as the DAC. So, even if the file is a lossless format, the phone's inboard DAC and amp will make it tough to compete with your iPhone 'transport', as Wadia called their dock.
That said,
averscds, you may find the phone is adequate for your purposes. You would have to decide whether the difference was 'major'. In that case, for you, there is no need for a $20K cd player. For others, the use of a phone's analog output as a source is not an option. If that person also has the $20K for the cdp, then the cdp might be their preferred source. That is for them to decide, for their own use, and expenditure.
I see that you have only recently joined. Just a word of advice from your friendly neighbourhood admin. Every person here finds their own path to audio nirvana, whatever is right for them. No matter where that system lands, on the cost spectrum, it is the value to that person which is important. If one is happy with what they have, then nobody should be ridiculing the amount spent, whether the amount is large or small.
A word to the wise, for all our gentle readers.