I agree, however, the teams where people don't need to read the audience, and can just freely present problems whenever they want without fear of repercussions

I agree, however, the teams where people don't need to read the audience, and can just freely present problems whenever they want without fear of repercussions are the most productive, in my experience. The management team must be "thick skinned" enough, though, to be able to take the blame and work on the problem. Maybe talk in private to the person about the tact. Of course, I'm not going to try, just personal observation.