Some parents don't see the point because they love their provider and feel like they're really on the same page about the birth. The problem is, you hire a doctor or midwife for one of the most important events of your life without ever having seen them actually do it! Coming into a prenatal appointment with a birth plan really lets you have a conversation about exactly what they do and do not do at births.
Another barrier I've heard to birth plans is that couples think they can just advocate for themselves at the time. The problem is, labor is not a time a woman can -or should- be thinking through options and conversing with strangers. She needs to be focusing inwardly on what her body is doing. Especially at the end of labor she often becomes very compliant and will just do what she's told because it's just too much to argue. With my second birth I thought I didn't need a birth plan, but boy was I wrong! It was probably my most textbook birth, but also my least favorite experience because I felt pushed around and ignored.
When you think about it, a birth plan is really just as much for your doctor or midwife as it is for you. Most health care providers really want you to be happy with your birth, so they'll bend to your wishes to a certain extent. The birth plan is not about making demands as much as just communicating your desires so they know. After all, it's really not fair to be upset they didn't do something you never asked for! If they seem unreasonably unyielding then it's a good sign you're not a match and you can look for a provider who won't have to feel uncomfortable following your birth plan.
I'd ask you to take a look at this article about interventions that are often overlooked. For more about how to write a clear birth plan and what kind of things to put on it, take my birth class!