Have you ever noticed that on projects RASCIs are usually referenced when relationships between teams/functions are irretrievably broken down?
Referring to the RASCI is used as a deflection. What's needed is a real meaningful conversation with the wider team about why certain things aren't being done and how the barriers to get those things done can be removed.
Like all project documents, the RASCI is only as good as the genuine intent and commitment to execute on what the RASCI states i.e. it means jack to say that 'x person' is responsible for delivering 'y thing' if 'x person' is not genuinely committed, confident, and competent to execute the task.
The answer isn't in the RASCI it's in the conversation. Maybe a difficult one, but you have to have it to get to a more functional 'other side'. In my experience, the hardest environments to operate in are always the ones that don't permit the necessary conversation.