Leo, CD players have been such common consumer items for so many years now that we tend to forget how much goes on inside them and how diverse the parts of a player are. There are servo motors and laser optics in addition to digital ICs. And then the results of those things get fed to analog circuitry which we expect to have an extremely wide dynamic range, insignificant distortion, and no audible interference from any of the other parts of the player. That's a tall order.
There is a basic audiophile principle which says that "separates are always better than combined units." That principle is based mainly on assumptions about the economics of design and production, and also on the fact that instead of just buying a Pioneer or Kenwood receiver off the shelf, it's more fun to obsess about a separate preamp AND separate tuner AND separate power amp! That approach keeps the hobby going whether it is technically justified or not.
In the case of CD "transports" and outboard DACs versus integrated "CD players" one big problem is that the S/P-DIF interface used for connecting the two separate units is designed backwards: it feeds the clock signal from the transport to the DAC, instead of putting a stable clock generator in the DAC and letting that control the transport. So now all outboard DACs have to deal with jitter issues that are ultimately caused by Sony and Philips' desire to let a single cable be used for this type of connection.
The one advantage which a separate DAC unquestionably does give you is isolation from whatever junk may be leaking into the power supply rails of the analog circuitry from the spindle motor and the optical carriage of the player. In some players, that can apparently be audible to some people under at least some circumstances.
There is no reason that an "integrated" player couldn't take care of this problem even in the middle price range. But even now, years after these issues became public knowledge, apparently some of the highest-priced players with the fanciest-sounding features (oxygen-free this, fully discrete that, ultraheavyweight the other thing, etc.) continue to have some audible remnant of this problem, so that price isn't necessarily an indicator of what to expect.
