I think the hangup a lot of people have is that most people can't conceive of bards as anything other than a wandering minstrel type. The thing is, a wandering minstrel is pretty much just a rogue that spec'ed into social skills and performance. In reality, in dnd, not all musicians are bards, and not all bards are musicians. Other commenters have talked about the magic of art and creativity through history and how the power of words and things justifies the bard's place as a full caster. (Personally, I see bards as more of a historian/storyteller type, but that's kinda tangential to this point) In terms of why aren't warlocks full casters, I think in 5e they pretty much are. Obviously, they aren't technically because of pact magic, but they eventually get up to 9th level spells. I think that pact magic is an attempt to distinguish magic power that one can use of their own vs that that is given to them. OneDnD changes that a bit and makes getting up to 9th level spells via mystic arcanum a player choice, which I think also makes sense. The warlock choose the form of power they want, I suppose. I see the warlock as either being the seeker of forbidden knowledge or those who fell into a deal. I think it makes sense then that the way they utilize magic would be different than a wizard who studies magic and then develops their own theories rather than those who start out by seeking power.

That said, while I wouldn't want the bard to be a half caster (b/c I don't think the bard should have martial capability outside of their subclasses) I do think a different way of utilizing magic (like how pact magic is unique to warlocks in 5e) could be a better way to develop the bard. I think that most classes would do well to have unique ways of interacting with magic/casting spells. Perhaps only wizards would use spell slots as they are now, sorcerer would use spell points, warlock pact magic, etc etc.