How is that "too late"? If it's a lossless copy on your computer or DAP, if you can stream that lossless copy as it is (and for high-res, no downsampling involved), then it can't be "too late" since you're sending out a digital signal. You'd have to be using the crapiest components/circuits to actually introduce enough degradation or noise into the signal that using a DAP's or laptop's DAC and therefore analog output stage would be preferable over a dedicated, DAC with a redbook-standard 2V output.
Yes, in most cases, it's not really the DAC chip but the analog output stage that makes the difference, especially if you compare a headphone out (if it doesn't have a real line out) to a fixed 2-volts, very low noise, low level (in some cases "high" level means amplified, as in speaker outputs) signal.
I'm talking about running an iPhone5, iPod 5.5, iRiver H340, Windows PC and/or MacBook as the source (primarily VBR MP3 files) to a dedicated headphone amp (MAD Ear+ HD) and then to a pair of Grado RS-1i's. There seems to be an implication that a good external DAC can "fix" the sound produced by the typically inferior internal DACs of most DAPs, basic CD players, etc.
Take note that such devices were designed with compromises and supposedly dedicated DACs have less of these. Conversely, many who stick to pure measurements will claim that this claim is just marketing fluff, but think of it this way - assume whatever device it is has no dedicated redbook-standard line output. A line input has different specs vs a headphone/earphone. Regardless of the specs on the DAC chips themselves, at the very least, a general use portable device running on a battery without a real line out can benefit a lot from a DAC chip that instead feeds a dedicated analog output stage sending out a fixed 2v signal with very little noise.
As for what you mean by "basic CD players," I'm assuming this means something like a ghetto blaster/boombox and not necessarily a dedicated CDP for hi-fi applications. So yeah, a dedicated DAC would be better than that, but a real hi-fi CDP, not necessarily. However, take note that not all CDPs or DACs for hi-fi applications sound the same (although theoretically, they all should) since some manufacturers deliberately color the sound or make compromises - I've tried some CDPs with of course fancier DACs and output stages than the basic, PCM2702 USB DAC built as an afterthought into my headphone amp and a bunch of them suck with headphones. Soundstage can be "larger," but they're all over the place - drum rolls around my head seems "wow!" at first but then you realize it's not realistic when the vocals are just ahead of your forehead (meaning the drums are positioned around the vocalist), or the drums are all in front of the vocals.
Basically, look up feedback but read between the lines. Right now the cheapest DACs (and actually, the most expensive DACs) I'd go for would be the ODAC and the Modi. Any other consideration against them would depend on whether the device I'd use with them would be compatible (I use my smartphone as a USB music server right now), or as I've been planning, a dedicated music server like the Olive 4HD, Cocktail Audio X30, Aune S1, etc. If you listen critically and without distractions like surfing the web (or worrying about your laptop's carbon foot print if you're using that), and can spend the cash on these, I suggest you look into these too.