The first, but definitely not the last, carol to feature a searing descant in the final verse. When sopranos sing the descant the altos have to sing the tune, which means that to sing carols as an alto you need (most of) a soprano range. Although if you’re me, you sing the alto part for most of it and then screech the descant, because it’s the most fun bit to sing.
(Although if what you want is a version of While Shepherds Watched that is fun to sing, you can’t get better than the Ilkley Moor version.)