What kind of a band, never plays music?

“A marching band”

A marching band is specifically known for playing music while parading, which directly contradicts the riddle's premise of a band that doesn't play music.

“A rock band”

A rock band is also associated with playing music, particularly in the rock genre, and thus does not fit the clue of a band that never plays music.

“A wedding band”

A wedding band refers to a group of musicians typically hired to play at weddings, which again involves playing music, making it an incorrect answer.