Great! Yes I see no issue with Prepared Bards having a limitless spellbook in their heads, especially when this Bard is supposed to be "Legendary." Tell all the magic stories! Learn all the magic songs! etc.
Agreed.
My one issue here is that Inspire Courage is THE combat performance. If you're going to track any of them round-by-round, this should be the one, because the player rationing those rounds between combat effectiveness for their party now vs. saving resources for future fights is the primary daily concern/interesting choice for the Bard, perhaps even ahead of their spell slots. The main combat performance being in the "Oh I just turn this on and don't worry about it for the rest of the day" bucket defeats the purpose of having a round-by-round resource in the first place.
I get that, but you're talking about a rework of a core class referring to one of the most niche subsystems in the game from fairly late in PF's run. And UI being available to people isn't really the point; there's a mental real estate issue whereby Bard is a class you can reasonably expect people - especially new/inexperienced people - to want to pick up and play from just a single book.