Inspire Courage should boost Morale, not Competence, and also boost skill checks, like Good Hope, replacing Inspire Competence altogether.
The realm of the Bard is emotion, not expertise. This would boost relatively underplayed classes like Sensei, Tactician, Vanguard, and Tactical Leader who could get a competence boosting performance. It wouldn’t be called Inspire Competence because spirit is the heart of morale and often competence is at best orthogonal to it.
This would allow Good Hope to function as a “good enough” replacement for that song, freeing up the Bard to use the other songs which have a hard time competing with Inspire Courage now because it’s such a uniquely (irreplaceably) strong effect.
Since there are other classes who can produce similar Morale boosting (like Camellia’s ability or Cavalier) and this change would create other ways to boost competence Inspire Courage would be less of a “must have” ability.