I don't know if the explanation holds, but I believe there were writer statements in prior editions that Alchemical charm prereqs sometimes reflected Autochthon's inhuman understanding of humanity in the same way Sidereal charms reflect the Maiden's often unusual takes on abilities. "Love is X"
I can see a bit of that, in that it is very much treating music and other kinds of performances as a tool to control people and make them feel/think a certain way. Like, a mode of encouraging social cohesion and making people better and more cooperative workers.
In this case it's also specifically just a charm about playing music to achieve different magical effects being found in a tree with several basic social influence boosting charms beforehand, which can all be used to boost more typical performance rolls, since those use the social influence system already. It means that, yeah, to get the flashy high powered bard shit you need to invest in basic competency charms beforehand, and have the whole suite installed in this case. That charms to make you superhumanly good at talking to people also make you superhumanly good at singing, dancing etc. is just a function of how Attribute Exalts work. "Oratory" is even a standard part of the basic performance ability.
Like...
Perfected Leadership Algorithm boosts social Influence rolls made with Charisma, generically. It even has a submodule specifically for Inspire rolls, the most common kind of roll made with Performance.
Perfected Union Patterning is a charm to boost social influence used, specifically, "to improve relations between members of two groups". This can be a verbal negotiation, or a concert -- it even has a built in "ignore the penalty for group influence" feature, which is something that Performance only has built in for Inspire actions.
Electric Fervor Inspiration is a charm to reset social rolls, which is, once again, applicable to performance, because performance rolls are social influence. Specifically, it's about a quirk in 3e's social system where if you fail with a line of argument or a social tact, you cannot then just try it again and again until you brute force them into believing or doing what you want, and have to meet a specific reset condition to try it again. In the case of Inspire rolls, you outright cannot try it again for the rest of the scene. This charm lets you bypass that through the literal magic of being a state propaganda robot. Say you sing a song about the virtue of honest hard work and cooperation etc. and you whiff the roll and the group of hungry and tired workers you are trying to convince to go back to the assembly line are unaffected. With this charm, you can simply sing the song again (or come up with a new verse or whatever), but
harder, and it might actually work.
This leads to
Perfected Harmony Amplifier, a charm that lets you sing or play music that grants actual magical effects in of itself. Like, in the example I made up directly above, one of its submodules is
Thousand Work Shifts Ballad, which not only motivates the hungry/tired workers, but supernaturally makes them feel less tired and hungry and lets them work better despite their physical condition.
I think this progression generally makes sense if you have a decent understanding of how the social influence system works.