I worked at a place like that. I wasn't even aware of the problem. It was just how things were.
One day our director called a meeting and announced that our whole department had a serious issue with interrupting. He noted the results of interrupting each other (not hearing each other out, drifting off topic, just being seen by the rest of the company as jerks). He laid out a bunch of rules for meetings, discussions, etc and he policed them for a few months.
It mostly worked as everyone (even the interrupters) saw the benefits pretty fast and the urge to interrupt seemed to fade as everyone knew they'd get to get all their words out of their mouth when it was their turn. Meetings even went faster.
Might be worth probing if your manager or any leadership feel like it is a problem / what the impact of this communication style is.
You can still bring it up to them as a problem that you have noticed where "some people" get overeager and interrupt others. mention the downsides and ask if he can help change the culture. You don't have to point the finger at him and it helps to enlist his help rather than complain.
You can try, but unless they (perhaps privately) realize they're part of the problem, I expect they'll end up verbally condemning interruptions while sabotaging any real attempts to curtail it, largely but not entirely by continuing to set a bad example. Is there a way to make this strategy actually work? By which I mean, have people actually seen it work in the long term? I'd love to be proven wrong.
It depends on their relationship, and the workplace and overall culture they grew up in. For various reasons, not everyone will be comfortable directly pointing out a flaw in their own boss.
I'd say that without knowing more, it's better to advise the safer and more diplomatic approach.
It is totally possible that beeing direct leads to the polar opposite of the intended result. This is something that can happen and it entirely depends on the people involved.
So some of use have learned how to recognize that type of situation and how to deliver bitter pills of truth without risking a job you might otherwise really like for it.
Be direct if you can, but don’t stay silent if you can’t.
Mostly about anyone adding something had to tie it to what the other person was talking directly, wrap it up with a summary and sort segway it back to the origional speaker.
Generally the meeting holder called on people and such.
Lots of "let's address that at another time" kind of stuff from the person holding the meetings.
Meetings had agendas.
After that it sort of bleed into how most conversations went.
One day our director called a meeting and announced that our whole department had a serious issue with interrupting. He noted the results of interrupting each other (not hearing each other out, drifting off topic, just being seen by the rest of the company as jerks). He laid out a bunch of rules for meetings, discussions, etc and he policed them for a few months.
It mostly worked as everyone (even the interrupters) saw the benefits pretty fast and the urge to interrupt seemed to fade as everyone knew they'd get to get all their words out of their mouth when it was their turn. Meetings even went faster.
Might be worth probing if your manager or any leadership feel like it is a problem / what the impact of this communication style is.