Don't confuse 2 issues. The question was about ditching a CDP, not about ditching CDs. Buy a CD and rip it to local storage and listen to it sound better than it would on a CDP. I do not have a CD player, but I do have hundreds of CDs and I'm still buying them regularly.
I think the above point (made some time ago now) is still valid but there are other combinations as well which do not involve downloads or streaming.
My silver disc purchases have for some time been on blu-ray, some video (all opera - 24bit/48kHz)) but others hi-res audio-only (24 bit/192 kHz). Obviously these cannot be used on a CD player, so 2 out of my 4 systems have Oppo universal players which I use to play not only blu-ray video & audio, but also SACDs & CDs.
A 3rd system has an Arcam blu-ray player for both video & hi-res pure audio (but cannot do SACD on this system), but it also has my only (remaining in use) CD player, a Rega Saturn-R, but this also has built in digital inputs - effectively a Rega DAC built-in.
A 4th system (which is in fact my main system) only has an SACD player for recorded music (no TV on this system), but also has an FM tuner (as do 2 others of my systems) & an Audiolab M-DAC+ which has almost every type of digital input there is. All my CDs (including hybrid SACDs) are ripped onto my Apple Mac Pro computer & copied onto 2 i-pods, both used with Oppo HA2 (/SE) headphone amplifiers/DACs which can be used for not only portable music, but also for headphone listening from my main systems as they have an analogue input.
I do have one CD-only player, a Quad 99CDP (which incidentally has 6 digital inputs, 3 optical & 3 co-axial but no USB) but I retired this in favour of an Oppo 105 so that I could create space for a turntable. I also have a second turntable on one other system.
It is generally assumed that the decline in sale of CD discs & players are the same thing, but this is not so although I think it is absolutely certain that both will continue to decline, but I think discs will outlast the CD-only player (too many alternative types of player) although these will be various types of silver disc. As for down-loads & streaming, these will continue to compete against each other, & vinyl will continue its re-birth as each new generation "discovers" analogue. Last but not least, FM radio will start its revival now that the BBC have come (partially) to their senses.