Stuff that only works in combat can be weird in terms of how long it takes for the game to realize that you're "in combat". But you're right that aside from that fact, it would be a clear improvement to just have the songs not deal damage and be combat-only. Personally, I would also accept an 80s cooldown on MB and AP, which I think overall would do more good.

SE just hasn't prioritized Bard QoL concerns, is all. Other than, for some reason, making a couple changes nobody asked for in 6.1, while ignoring issues that are actually frustrating people.

Presumably SE just doesn't have the bandwidth to properly care for all 20 jobs at this point. It's a guessing game of which jobs they're going to decide most need attention at any given time, and then a second stage of guessing at whether they actually understand what a job's needs are.