Something to add to what Andy said, is that, if the input impedance of an amplifier is sufficiently high, which most are, then you likely wont get any current gain from a headphone amplifier output stage anyway.
What people are referring to with a "true line out" is only a single, voltage gain stage after the DAC, rather than the dual dual-stage, voltage and current amplifiers used for headphones.
Chord DACs aren't the same. The reason for this is that one of the critical aspects of a regular DAC is for the first gain stage to filter out high-frequency noise that is output alongside the music. That isn't an issue with Chord DACs, so they only require one gain stage for everything.
This sounds appealing on the surface, but would not really be sensible. Converting to DSD requires a lot of power, and the quality of the conversion would suffer in a portable device. It would also not produce any useful sonic benefit, but just move complexity elsewhere, switching from a complex R2R ladder to a complex high-frequency circuit, converter, and filter. You could, conceivably use DSD upsampling with something like Onkyo's HFPlayer on a phone, but that tends just to make the sound somewhat soft and blunted, depending on what it is fed to.
Something people forget is that real, live music sounds raw and edgy. What people call "analog" is the opposite of natural. It's nicer, in some respects, to listen to music that has been softened by whatever means, but if you listen to even something as simply as a drum set relatively close, you realise that most music has had the actual dynamics grossly muted, even at best.
Holo Audio does this by using a cheap, generic over-sampling chip, which nobody in their right mind uses to listen to music with (as using it sounds awful in my experience) just to get good measurements for standard test signals. Basically, they are gaming the system.
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