The thing that actually sets the volume is the amplifier, which is after signal has been converted from digital to analog. In this case your monitor. USB allows for volume control to be passed to the device at the end of the chain. HDMI possibly too via CEC, but you need everything in HDMI chain to talk CEC. I'm not sure if DisplayPort allows for volume control.
In theory, there's no technical reason why volume control commands could not be sent along digital path as long as volume control on the analog side is "soft" (e.g. via on-screen controls on monitor, up/down buttons, or fly-by-wire knob). This is effectively no different than using good old IR remote to do the same thing. If the volume control on the analog side is "hard-wired" (e.g. you directly turn good old potentiometer to adjust the volume), you are out of luck (and generally, such devices can't have good old IR remote control either).
That is in theory. In practice things can and do go horribly wrong sometime. I've a pair of Dell USB speakers attached to my monitor. Volume control is, of course, enabled. Except when I set it to "one bar" using keyboard, it's way too low. When I set it to "two bars" it's ridiculously loud. "Three bars" and the windows are rattling. I never dared to set it to "four bars".
I also have NuForce uDAC-2. Which is USB device. With hard-wired volume knob. My Mac really shouldn't allow me to control volume on that thing via keyboard. But it does!? With expectedly horrible results.
The software that attempts to "fix" this by messing with digital audio data before sending it on its way is generally horrible idea. It degrades audio quality. And you have effectively "double" volume control. It's especially horrible if you dial volume down on the digital (source) side, then attempt to dial it up on the analog side. Just say no to such applications, no matter how convenient and "problem solving" they look like.