Given that they've been in continuous use for centuries I question the conclusion that they're not effective, but I'm open to altering my opinion backed-up with data.
> Bear bells may be a popular item to put on your backpack, but they don’t effectively warn a bear you’re in the area. Bears won’t hear the bells until you’re too close. Yelling, clapping, and talking are more effective ways of alerting a bear to your presence.
> In the most advanced testing, bear biologist Tom Smith jingled bear bells in varying volumes in front of brown bears in Katmai National Park. Regardless of how vigorously he shook, 15 different sets of bruins ignored the bells. And yet they snapped at attention the second he broke a pencil in half.
It's not that the bells definitively have zero value, but their effectiveness has been questioned enough that there's been a shift in opinion about them over the last couple of decades.
Mountain lions are avoidant at all times unless it's a mother with cubs and even then they'll let you know well in advance.
Otherwise, just normal conversation, your smell with even a light breeze, and the vibrations on-trail will alert all animals to your presence.
In other words, the "trail music" theory is bullshit. They just want to listen to their music.