Quite a question Karen!
Firstly I believe that communication has evolved rapidly over the last 10 years. The business communication skills that were taught and widely accepted in 2009 have been radically changed with technology and mobility. New graduates today are "hyper connected" and the shorthand of a tweet or an Instagram story requires a different ability to convey a message than previously. If I need to compress something to 140 characters then I have to view my message and my wording much more carefully than a verbose email or memorandum. The world in which new grads learned to communicate with peers is certainly not the same as the prior generation.
That said the gap between the newer communication preferences and modes and the prior generation does indeed create a barrier to effective business and professional communication efforts. A 50 year old would likely accept a company handbook in paper form at orientation. A 22 year old fresh grad would much prefer to have the employee handbook in digital form so it can be consumed when convenient for them and searched for key concerns.
I believe one of the main themes of your question is how the differing communication styles translate to leadership and performance. This is something that has changed very little in spite of the ever evolving vernacular and technologies. Leaders must be adept at not only identifying issues and opportunities within their team but the pivotal skill that sets leaders apart from managers is the ability to communicate at many levels effectively. When leading a meeting of interns and new graduates it would behoove the leader to steer clear of voluminous binders and printed business cases in favor of digitally consumed materials delivered prior to the meeting. As homogeneous age groups are exceedingly rare in most businesses the leader must also prepare for all participants and communication styles. Visual versus tactile versus note takers- each much receive the intended message as closely to the speaker's original idea as possible.
Would there be a gap or barrier to promotion if a younger employee showed promise with their duties but was unable to adapt their speaking and communication style to a senior leaders conference? Yes indeed and it would be a great opportunity for that individual's supervisor to approach exactly that subject with the rising talent to help them along.
Training and ROI measurements on that raining gets much deeper into an expert corporate training curriculum. I think the key here is to first identify that there is a gap in communication not skill or talent and very specifically leadership ability.
On my teams I prefer to put staff into situations where they have an opportunity, even if it is uncomfortable, to present an idea or solution. I do not give them a specific mode, just that it will be presented at the next staff meeting. Some go to PowerPoint slide decks with bullets and graphs, others prepare handouts and talk about their findings. Yet others compile multiple formats into the team intranet site with dynamic content and links. During each of these varying presentations I am scoring for completed ideas or thoughts, cleanliness of spelling and grammar, and reception by the audience. If there are blank stares and minimal questions then the presenter missed the mark. Following the presentation I follow up with each and give them my feedback on what worked and what I felt maybe didn't so they can develop and work on their own personal style.
As you can tell from the length of my reply I am one that prefers to write out my thoughts versus directly speaking. Over my career I have worked diligently to improve my speaking skill to come closer to my written communication skill. Some of my changes have come following feedback from superiors and peers, others I made reviewing my own recorded presentations. Ultimately communication is the glue that binds an organization together. Without effective communication all the good intentions and skill cannot drive toward the company goals.

When people sitting in the same office communicate via email, one knows the world has gone crazy.

Companies have tried 'email free days' in order to encourage people to talk more.

If people always see the boss hunched over a screen, they will see that as the norm.

I remember the concept of 'management by walking around' and think it is more important than ever today. Talk to each other!