Your main problem with built in headphone amps on CDPs is that they tend to not really be good headphone amps. At best, there's Marantz with a headphone driver chip and typically a better power supply design, but it's still basically just a little bit better than a DIY portable amp with one 9v battery, and the Philips headphone driver chips they use have a high output impedance. My Marantz CD60 was good enough with my HD600, but my SR225 sounded like tin cans on them (and actually my 9v CMOY was a lot better).
On top of that you'd have to buy a Marantz CDP, but by contrast you could just get a DVD player from a store (or use whatever computer you typed that post in, provided it's quiet enough) as a source unit for a DAC-HPamp or a DAC and a HPamp. So say you use your computer or laptop and its quiet enough at idle, you can get the Schiit Modi2 and Vali2 for less than a CD5005.