Not going to argue about AGM vs Lithium -- need more details to weigh in on that. The only point I wished to make is that the power source of the audio amp, whether Class A, AB, B or D can matter -- in fact it usually does. A Class D "digital" amp doesn't allow you to escape having a decent power supply. Consider the difference between a 16ohm load, 8, 4 and 1 ohm load (speaker) -- yes I have (fantastic) 1 ohm speakers. An audio amp is supposed to be have a particular VOLTAGE gain, regardless of load -- it is designed to be a voltage amplifier.
Consider an amp with a 28X gain. That means that, e.g. if you put in a 1V p-p audio signal, it may be expected to output a 28V output. And if it is rated at 100w into 8ohms, that would be 3.5A, 100watts = 28V * 3.5A (into 8ohms). Now instead of 8ohm speakers, connect 4ohm speakers, the same amp is now expected to deliver 7A while maintaining the 28V output, (and yes that means it is outputting 200w). Now connect up 1ohm speakers, the same setup is suppose to deliver 28A into the 1ohm loads to yield the 28V output, yielding 800watts. The point is that it really matters that not only is the amp up to delivering that kind of current, but the power supply (battery?) has to deliver high currents also. And it doesn't matter if the amp is "digital" or not. Those output MOSFETs still have to dump that kind of current into the loads while maintaining the specified voltage. The lower the frequency, the longer the MOSFETs have to keep dumping the current into the load. Amplifier class is about the conduction behavior of the output stage, the amplification required for proper output signals remain.
Whether some AGM is better than some lithium battery, it depends, but it certainly *can* matter. Many bad audio amps are bad because of their power supply. In this case, the audio amp being powered by the DC-DC converter, it shouldn't matter what the 12V battery is.
Agreed wholeheartedly. My point being, the waveform is generated by the Class D amp, not necessarily the input power source. So yes - the MOSFET needs the correct input voltage & current, but the idea that the li-ion battery can do so "cleaner" the AGM doesn't make a hill of beans of difference in our case here - the AGM is more than sufficient. Either the MOSFET gets what it to create the correct wave, or it doesn't. That's my argument with the digital class amp; no more, no less. I agree with you - the battery still needs to deliver plenty of current at the correct voltage. But the idea that the li-ion does so "cleaner" - behind a DC-DC converter, doesn't mean a dang thing in this application.