What we do, and I think it works for us.
Project update have to be given by project owner, even in situations where majority of tasks are performed by others. If owner of the project thinks that it is not one of his roles accountability to work on the project he can ask appropriate role to take over the project.
What we have sometimes, that the outcome/project has more sub-projects, which are taken by different roles. Than there might be several updates from more people.
About rigidity, we have same critics, but in my opinion it is ok, people are people, we do not like to go out of our comfort zone. It is important that facilitator take into account holacracy maturity of the team and adjust his facilitation to it.