Just to be clear, this isn't playing between songs, it's more over-embellishing everything. We play mostly originals in a style somewhere between ska and reggae, and there are little off-beat snare hits and fills, and cymbals, and all sorts, all over the place - sometimes the singer will call for us to quieten down, which he does with no problem, but still puts in little bits all over it.
There's nothing necessarily "wrong" in what he's doing, it just annoys me We've had drummers who are more restrained, and it leaves space for the rest of the band to work in, and more of a groove (IMHO)