A reduced CD allows it to be used more frequently which is always good; multiple times in long fights or even just to have it available every pull or so.
At end game a lot of Minstrels have dedicated heal and dps weapons and there are only 5 majors really valid on a heal legendary weapon and TS CD is one of them so it often gets included.
I was lucky enough to get a 3rd age with 5 majors so I use them all on my healing weapon.
Shorter CD usefulness is always situational ofc but its nice not to have to worry about saving skills - I fire up TS often as a replacement for Chord of salvation to give me time to tier up ballads after a coda for example.