All of these analogies are way off base.
A good DAC is a good DAC, end of story. Just like a good phono cartridge/preamp, or tape deck, or whatever.....the source output quality is not a function of its output voltage.
Virtually all DAC's convert the digital signal, regardless of format, into an analog signal at the same output voltage--nominally, 2.0 Vrms for a "0 dBFS digital signal" (meaning, when the data stream is at the maximum amplitude that can be encoded on the CD). Some are spec'ed for 2.1 Vrms, some put out about 2.4 Vrms, but in terms of amplification or ultimate loudness, that isn't much of a difference. In other words, almost every DAC produces the same signal strength at the output given the same input data.
Now, the quality of the digital-to-analog conversion process can indeed differ, and does to a significant extent. But that's not necessarily tied to the degree of amplification of that signal.
Headphones are certainly much more sensitive than speakers, and DAC outputs are not primarily designed to drive transducers of any sort, However, if you connect a pair of 300 ohm cans like HD600's directly to the output of most DAC's or players with opamp output stages (most of which can swing more than adequate current to drive hi-Z phones) and play a CD, the volume level is fairly loud.
HD600's, for instance, would be playing peaks at 104 to 106 dB, if I recall correctly, and the power required is only about 13 milliwatts (0.013 watts.)
On the other hand, if you have a 100 watt/ch amp driving 8 ohm speakers at full rated output on peaks, it's pushing out just over 28 Vrms, and 7700 times as much power as is driving the cans in the example above--but depending on speaker sensitivity and the room, you are likely only hearing the music at about the same perceived loudness as on the cans. And unless you have some extraordinarily good speakers, you are hearing fewer details than on the headphones at the same preceived voume level.