In 5e, after a bard has joined the College of Swords at 3rd level, when–if at all–would they need their instrument(s)?
At 1st and 2nd levels, they would have used musical instruments as spell casting foci, but for those who join the College of Swords at 3rd level, "If you’re proficient with a simple or martial melee weapon, you can use it as a spellcasting focus for your bard spells".
So, no need for a musical instrument as a focus for spellcasting.
As for bard abilities, Song of Rest, gained at 2nd level, is brought about through "soothing music or oration", and for Countercharm, gained at 6th, "music notes or words of power" are the means of achieving the desired effect (PHB p54). In both cases, the option to of speaking–oration or words of power–means that a muscial instrument is not needed.
It seems strange that a the defining feature of a class becomes vestigal.