Music is not the entirety of the bard's identity anymore than it was for Shakespeare (AKA "The Bard"). And, in fact, the dictionary definition of "bard" is a poet. Music isn't the core of the Bard class--Performance is. And that can be open to interpretation. And, even then, it doesn't even necessarily happen in combat.
Let's look at the 5E Bard's actual write-up and see how much music itself is ingrained in the class:
Spellcasting: "You have learned to untangle and reshape the fabric of reality in harmony with your wishes and music." So, yes, here music is mentioned. But music can be verbal, and, in fact, the verbal component of bard spells in 3E was recitation or singing. We also learn that a musical instrument can be used as a focus for spells. In 5E, foci are used as replacements for material components. Material components can be used with the same hand that is performing the somatic components, and only one hand need be free. That means a focus need only be used with one hand when casting. I don't know many musical instruments that can be played with one hand. In this case, the instrument serves as a rod, staff, orb, sprig of holly, or whatever a focus might be for any other class. It need not be played, but it can be. I don't view it as a tool so much as a symbol to help visualize and center the mind. In addition, a spell component pouch can replace the instrument as a focus.
Bardic Inspiration: "You inspire others through stirring words or music." Recitation or even just a pep talk can serve the purpose here. Music is a choice, but not a requirement.
Song of Rest: "... You can use soothing music or oration to help revitalize...." Again, music is a choice, but not required.
Countercharm: "... You gain the ability to use musical notes or words of power to disrupt...." Same as above.
Magical Secrets: Spells from other classes become Bard spells and, thus, are cast in the same way as above.
Cutting Words: "... You learn how to use your wit...." No mention of music.
College of Valor pretty much just adds on to combat ability and modifies already-existing features.
So, as you can see, music is not intrinsic to the class at all.
Sorcerers are, by their very definition, born into magic through some sort of bloodline. Of course it is entwined in their very being; it is in their blood.
As I said above, it's not music, but Performance that is the core of the Bard. But don't mix that up with the Performance skill. (Though, I would go on to say that a Bard without proficiency in Performance does himself or herself an injustice. Even so, Proficiency in that skill is not needed as long as the Bard has an instrument with which he or she is proficient.)
