A more powerful amplifier will be beneficial if it allows headphones (or speakers) to play with less amplifier distortion, either at the same volume or at louder volume. You can split this out into different cases, i.e., same volume with less amplifier distortion, or louder volume at the same or less amplifier distortion, etc. But no matter how you split it up, it is truly about avoidance of amplifier distortion, and other than this, there isn't a reason for a more powerful amplifier. (It is tempting to say that a more powerful amplifier will simply allow the headphones or speakers to play louder, but this statement is sort of meaningless if it isn't qualified in terms of amplifier distortion.)
The problem with the notion of "scaling" is that it isn't associated in a well-defined way with avoidance of amplifier distortion. At face value it seems to suggest that even if you don't hear distortion with the amplifier you are using even when you play it as loudly as you like, the sound of the speakers or headphones will nevertheless be improved with a more powerful amplifier. This is a common belief among audiophiles, that you see when people talk about how a more amplifier is needed with some particular pair of speakers (or headphones) in order that the speakers (or headphones) will "open up". For no particular reason that is ever adequately explained, a more powerful amplifier is needed in order for the speakers (or headphones) to sound as good as they are supposed to sound, regardless of the volume level. This belief is very much one of those things that audiophiles believe simply because it is convenient. We (me too) like to buy a new amplifier when the newness of the old one has worn off, and we need some kind of justification for the purchase. On internet forums it easily becomes a meme that with such-and-such speaker or headphone, you need to use such-and-such amplifier lest the speaker or headphone will not sound fully as good as it is supposed to sound.
There is another reason, besides greater power, that it can make sense to use an external amplifier and not the one built in to your computer or phone. But it depends on whether the output impedance of the external amplifier is lower than the output impedance of the built-in amplifier. You have to investigate the possibility and not just assume that it is going to be true. This is possibly the better reason for using an external amplifier, again assuming that the external amplifier really does have lower output impedance than the built-in amplifier. Whether this reason or the mo-power reason is the better reason depends on the particular circumstances. For anyone who might not understand why it is beneficial to have low output impedance, the reason (one of the two potential reasons) is that high output impedance messes up the frequency response of the headphones (or speakers), except in the unusual cases where the headphones or speakers have an impedance curve that is essentially flat. If I recall, planar-magnetic headphones are supposed to have essentially flat impedance curves, in which case the output impedance of the amplifier doesn't much matter unless it matters for the other reason. The other reason is that high output impedance will eat some of the output voltage such that the voltage delivered to the headphones will be somewhat less than it would otherwise be. Regardless, there is clearly a reason why the impedance curve of the headphones or speakers matters and may play a critical role in the fully correct reason for using an external amplifier.