The second and third examples seem to be narrative descriptions of various uses of the bardic class feature Bardic Inspiration which also doesn't require any sort of focus or musical instrument. The M components for this spell have a specific cost (250gp worth of incense and 4 ivory strips worth at least 50gp each), which means a bardic focus can't be used to cast it, so in this case, if she is casting Legend Lore (and it sounds like it, from the narrative description) there is no bardic focus. The first example is most likely a demonstration of the bard casting Legend Lore, which has V, S, and M components. I also don't know that the examples need to exactly match what can be done in game, for the same reason - they're narrative examples, not gameplay examples. In the examples provided, I can just as easily see those as representations of the bard's class features rather than the bard casting spells. Not all spellcasting requires material components or a focus of some sort. That being said, the examples need not represent spellcasting at all. I see these examples (not just for the bard, but for all classes) as very good ways of showing how those classes exist in the world, what their roles are, and how they fit into the game from a narrative perspective. Is it reasonable to assume that RAW or at least RAI that the implication is that in the case of bards, they can use 1) their voice, 2) an improvised musical instrument, or 3) a bought musical instrument?ДЄnd if such an assumption isn't RAW/RAI, what are the implications to allowing it as a house rule? Maybe it is meaningless fluff, or maybe the implication is that those are all spellcasting foci. In each example, the implication is that the bard is casting a spell, and the implication is that the action of the bard is central to the magic, and at least to my reading, that the voice, sword/mail, and instrument are spellcasting foci. Laughing as she tunes her cittern, a gnome weaves her subtle magic over the assembled nobles, ensuring that her companionsвЂ™ words will be well received. The magic of his song fortifies and emboldens them. Humming as she traces her fingers over an ancient monument in a long-forgotten ruin, a half-elf in rugged leathers finds knowledge springing into her mind, conjured forth by the magic of her song-knowledge of the people who constructed the monument and the mythic saga it depicts.ДЄ stern human warrior bangs his sword rhythmically against his scale mail, setting the tempo for his war chant and exhorting his companions to bravery and heroism. You can use a musical instrument (found in chapter 5) as a spellcasting focus for your bard spells.ДЄnd yet on p53, the PHB in the introductory description of bards, gives examples of three bards:

Inspired by this question: Can a multi-class spellcaster have one thing be two different focuses?

Focusfixer vs focus magic