Closed Captions are incredibly important to me.
Without captions, I just can't really enjoy watching a tv program or a movie. I wonder what dialogue I've missed even when I can follow the action and plot. After a few minutes, if that long, I usually give up. I've found I give up even if it is a movie or a program that I remember from when I still had some hearing. I just don't enjoy it.
And it goes beyond a matter of enjoyment. Sometimes it is a matter of critical information.
When watching tv and a news alert, a weather alert, or an amber alert comes across the screen, I want to know what's going on. Sometimes more information follows along the bottom of the screen or the programming is interrupted. Sometimes the interruptions are captioned; sometimes they're not. In the case of amber alerts, I was complaining about the lack of information to someone when they informed me that the rest of the information that I felt was lacking was spoken only and wasn't written or captioned. So, I guess it was only important for the hearing portion of the population?
And it's not easy or practical to try and speechread totally during a tv program or movie because of camera angles and people speaking off camera or obscured. And "the best estimates are that 30% to 35% of English sounds can be speechread under the best circumstances." http://www.hearinglosshelp.com/articles/speechreading.htm But, that's only around 30% and the article goes on to mention that only about 23% of hearing impaired adults become effective speech readers.
So that leaves the majority of Deaf and Hard of Hearing with a necessity for captioning for enjoyment and understanding of programming on television and the internet.
That can really be hard for a hearing person to understand. I know it used to be for me. But, try watching tv programs or movies without the sound and without captions. You'll find yourself straining to understand what's going on. And how much you enjoy the movie, even one you've been looking forward to, goes down. Then, you start to understand how important captions are for people who can't turn the sound back up or on.