Well, incase if you did not know the bards who are from college of lore are best spellcasters in entire game
, when it comes versatility and knowing various spells. Basically 'red mage' on steroids. So saying spells are not part of bard's arsenal is same as telling figther's weapons nor armor are not part of their class
So even if you decide not pick any spells which asks saving throws (there is lot of them in bard's tree and other spell trees), having high charisma helps in class crucial skill checks and also boost saving throw which you got profiency in already (performance, deception, persuasion, are all charisma related). Also inspiring leader (even if lackluster as a feat) greatly benefits from high charisma modifier.
Also many healing/buffing spells have xdx+cha mod in them, so to serve in role of buffing or healing you need high charisma modifer (example heroism gives temp Hp per round based on cha mod alone).
Also one your important class features; bardic inspiration, numbers are entirely on charisma modifer (if got 0 charisma mod as bard you can only do it once per combat for entire day
until 5th level you recover bardic inspiration between short rests also). In 5th edition bards are solid support jack-of-all-trades class, in case lore bards their also most versatile spellcasters also.
So, do not dump your charisma as bard and use best stat for it. It's worth me trust me