You may know the difference between a DAC and Amp, but you clearly don’t understand what I’m trying to say. I’m saying that a DAC doesn’t have its own power output. It literally takes a digital signal, and converts it to analog. In order for it to add any power to the signal, it needs to include an amplifier. Otherwise, the signal will always be a little bit weaker due to the power loss from traveling through the DAC. Most DAC units have at least a weak amplifier for this reason, but there are some units that are just a DAC. And the Amp part isn’t going to be controlling the digital volume, i.e. changing the system volume on your device. It will operate on its own volume control, so regardless of how limited the output is from your phone, it will still be made louder as it amplifies the volume independently of the phone. A unit that is just a DAC doesn’t have any way to amplify the signal it receives, so it will never be able to make it louder.
You said explicitly that the android system will limit the output of any DAC, but that is wrong on multiple counts. The android system will not limit the output of a DAC because a DAC itself just 1:1 outputs an analog signal converted from a digital source so there is nothing to limit. The android system will also not limit the output from an Amplifier because it literally is not capable of that. That’s like saying your water faucet can limit how hot your water can get when you boil it on the stove. An Amp increases the power of the signal after it has already left the phone.
Even if it was somehow 10° below absolute zero, it would still be 10° above absolute zero