in most places (certainly on this side of the Atlantic), the phenomenon you are discussing does not tend to exist

If you move away from "domination of a session by the Chieftains' music" to "domination of a session by a specific source" then I have known it happen with groups that slavishly follow Carthy:Waterson interpretations of songs and similarly on Copper Family Songs. What is quite odd is that the Carthys, Watersons and Bob Copper at least - and I bet its true of the Chieftain's as well - would treat that approach with short shrift.    But Declan is quite right: the problem lies with the session players or singers, not with the source.

(I have no problem with the Chieftains being successful by the way, and have seen them in concert quite a few times, including in the last couple of years.)