We don't because we don't have the syllabus trained guys. To a certain degree. (we are a small club in a rural town) but for those that do. They absolutely train the systems.
So when our judo guy actually turns up for example. It is gi on bow in and do judo. It is not mma no gi judo throws.
I guess my understanding of what MMA is conceptually may be wrong. You literally do a mixture of different styles depending on the teacher and night?
Where I was thinking MMA was a coach that would teach strikes, kicks, grapple etc. based on what would work in the context of a cage\ring etc. Whether that coach had a background in a particular arts was irrelevant, but you would get the benefits of that knowledge.