The need for enough power to avoid (minimize) clipping distortion is not a myth. Just as the need for a beefy power supply and output section to handle difficult loads is not a myth.
While often referred to as dynamic range, the need for headroom - that is, power in reserve above the continuous (aka average) power output at a given SPL - is actually driven by the momentary/transient peaks occurring in the music. In a good recording, these peaks can be 12-15dB higher (louder) - or more - than the continuous signal level in a good recording.
So, for example, if your amp is pushing 2 watts on a continuous (RMS) basis at your chosen volume, it would need to be able to deliver 64 clean watts to handle a 15dB peak without clipping...and do so into the load presented by your chosen speakers. There are some who believe that there are also "micro-transients" that are so brief as to be difficult to measure but demand even more power (voltage).
BTW, dynamic range is the difference between the quietest and loudest signals in the recording, as opposed to the difference between the average level of the signal and the loudest portion. Similar, but different. As applies to a playback system, vs a recording, dynamic range is the space between the noise floor and the clipping point.
And headroom is the available power your amp has "in reserve" when running at a given continuous output level; that is, the power available to amplify the peaks - the louder portions - of the signal. As is probably obvious, as you increase your listening level (higher average SPL), headroom of a given amp shrinks.
Somewhat confusingly, there is another definition of headroom, sometimes presented as an amplifier spec. In this usage, it is the difference, in dB, between the rated RMS output of the amp and the output it can produce momentarily without clipping.
If you are interested in budget-oriented Class D amps, consider some of the Fosi offerings along with the Allo. The VR3 referenced above is getting a lot of very positive reviews, and tested very well at ASR. Comes with 32V or optional 48V power supply, for under a Benjamin all in.