If played subtly and musically, the piano can add a lot although many piano players are florid and some intrusive. Played simply and appropriately, with proper fill-ins and sparse chord sequences and at a volume that doesn't overpower the other string instrument(s) it can add a great deal.

I second the motion about the Cape Breton players, a highly syncopated, almost
early jazz accompaniment that they do adds so much to the dance.

Of course the Blues players, Memphis Slim and others could qualify as trad.