Depends on the role of management in the company. At some companies there is a bright line where managers are expected to _not_ participate directly in the technical discussion of how to solve problems.

So say, in such an organization, two teams each with a Staff Engineer are taking different and conflicting approaches, and neither Staff has been able to pursuade the other to their side? Often in this scenario it's extremely valuable to have a technically capable third-party mediator to help bring the two together.