As a story idea, I think that's totally fascinating and it would make an excellent story (omg write it), but societally, it just makes sense that there's no real reason for a Companion to strike out on their own. Being a Companion is an elite and highly respected position on the Core Planets and out in the black, a lot of time your only protection and recourse to the law would be having the bulk of the Guild behind you. "I am important and I have important friends so don't fuck with me."

The thing about Nandi was that she got no respect (even from Inara, to some extent) and she had no protection from someone like Rance Burgess. That's why she had to appeal to Inara in the first place.