I think you can join a group cash-only practice. It is just rare. It is hard for a cash-only private practice to fill doctors up with the number of patients, considering the limited number of referrals they get as it is.
And let us say, you are the rain maker, and the patients are referred to you specifically, it is then hard to tell them, "well, please see my associate. I charge $350 per hour but my associate only charges $250 per hour, and he/she is just as good as me." The first question the patients will ask is, "then why is he/she only charging $350 and you charge $250." Don't forget. The patients are referred to you only and are willing to open their wallets. They get suspicious that your associates are just not as good and they will hesitate.
Then once you raise the associates' rates to your rates and they are now doing well, then they want to leave and open up their own practice.
There is a reason why most if not all cash-only practices are still solo practitioner based.
In my area, I have seen many cash-only practices bringing in younger associates or even nurse practitioners at lower rates. I think the longest these people stay are two years at most. And they are off on their own, and the "group" basically got broken up, back to square one, i.e. solo practice again.