That's only a half-truth. DACs are all "amplified" as well, from its initial I/V conversion to its line-level (usually 2 Vrms) amplification. The only difference between a DAC and an amp is that the DAC only needs to supply a full scale signal with as wide an SNR as possible, while the amp actually drives a transducer. Being a device driver and not a line driver, an amp will have higher voltage drive, and lower output impedance. At full scale volume, if the SNR is not significantly degraded, then there's no reason why an amp's output cannot be used to drive another amp.
If you examine the HP and HD, you'll find that it uses the same opamps, namely the AD8397. The difference is that in the HP drives the opamp to 3.5 Vrms (at 0 dBFS), while the HD remains at line level 2 Vrms. What's the difference in noise output between an opamp driven to 3.5 Vrms and 2 Vrms? Is there a significant enough SNR penalty such that you want a dedicated DAC? These are the questions that should be asked.
From experience, it seems that the full scale output of the HP is clean enough to act as a DAC. It's not as clean as the HD's, but the difference doesn't really have practical benefits. You can step down the volume on the HP to 2 Vrms and get an equivalent output level as the HD, but it will now have been digitally attenuated by a little bit. I don't know what the numerical differences in DNR are.