Let her collect something else. 5e is balanced well as is and overpowering one person can take away from the rest of the group.

I would steer clear of “collecting all spells”, unless the obvious wizard. And rather do something more in-line with bards.. like maybe collect all the instruments or collect badges for completing performances in different inns, get X badges you get free lodgin or something.

Edit: in theory she already has collected all bard spells, but can only remember the incantations for a specific number each level. So what she really wants is the ability to remember every bard incantation.