Well, here are a couple ways that I feel trying to navigate a poly lifestyle improves our general communication skills in relationships in general.
Poly kind of forces us to get some open discussion out on the table about two very sensitive subjects. These are subjects we often avoid to some degree - at least to dig in deeply & honestly. There are carefully constructed masks & images we learn to present to people to cast ourselves in the best light. We learn to tell them what we feel they want to hear/see. But that leaves important parts of ourselves hidden and some of those parts are critical to maintain healthy relationships with others.
The subjects are of course sex & love. Two very tricky subjects for most. They are words we use all the time but don't often take time to really understand & define.
Poly forces that to change ! If it doesn't, the house comes tumbling down on your head pretty fast.
As it does change you discover that the skills you learn about open, honest communication have a wealth of other applications ! In a nutshell, your communication style and approach will never be the same.