They impose disadvantage on saving throws against charm affects (which are very many of the Bard's cooler abilities)
Actually, they only impose disadvantage on saving throws against Animal Friendship and Hypnotic Pattern.
When you use the instrument to cast a spell that causes targets to become charmed on a failed save, the targets have disadvantage on the saving throw. This effect applies whether you are using the instrument as the source of the spell or as a spellcasting focus. (Dungeon Master's Guide, p. 176)
Spells like Suggestion do not benefit because they do not cause the targets to be charmed, even if they do not work against creatures that are immune to charm. For the same reason, elves and half-elves do not gain advantage on saving throws against Suggestion.
Furthermore, spells like Charm Person do not benefit because they do not require material components. A spellcasting focus is used in place of material components. If the spell doesn't require material components, you do not use a spellcasting focus to cast that spell, and therefore cannot use the instrument.
See:
Charm person doesn't benefit from an instrument of the bards, since the spell has no material component. (Jeremy Crawford, Sage Advice)
The only two spells that require material components and cause targets to become charmed are Animal Friendship and Hypnotic Pattern. The only spell that can be cast directly from one of the instruments and causes targets to become charmed is Animal Friendship.
That being said, Hypnotic Pattern is quite amazing, and the other spells the instruments offer are quite nice.