Because each is a secret cult, with their own agendas. It would be strange role playing a character, belonging to two, secret cults. The Mythic Dawn strove to transcend Mundus as the stars from myth, while the Dark Brotherhood is occupied by euphoric murder, which is their own way of transcending Mundus.
Would make a good comedy:
A: So when are we going to plot the downfall of civilisation?
B: (Checks agenda) How is Monday?
A: Next Monday? Well, on Monday I've got my secret meeting of the Masons.
B: Alright. Tuesday then?
A: No not Tuesday, I'll be executing the rites at the local covern.
B: Okay, well I promised the misses that I'd be with her on Wednesday so how is Thursday?
A: Sorry, Masons again.
B: Friday?
A: Illuminati.
B: Right... of course. Can you pick me up at eight o'clock again?
A: No problem.
B: How are you on the weekend then?
A: Sorry can do, city council.