I maintain that the Bard should be renamed as "Adventurer", a generalist class that has picked up a variety of skills on the road. In old Final Fantasy terms, he is a Red Mage. He has learned how to wear armor and wield weapons, how to cast rudamentary spells, picked up a wide set of skills, learned a variety of languages and about different cultures, and developed skills to communicate with people from all walks of life. His "Bardic Inspiration" and "Countersong" skills simply relate to his Leadership abilities and inspire his companions.
I'm not a super big fan of the idea of someone strumming a lute to cast magic, but that is me. But I was always a fan of the Blade-Bard from 2nd Edition.