My first birth was a HB transfer at a very NCB-unfriendly hospital. Having a birth plan in my file, signed by my OB, ended up being enormously important for me to get the closest thing as possible to the birth I wanted. The routines and procedures of the hospital were NOT in my favor, which meant that I certainly had to advocate for myself and the baby verbally during my stay, but having the birth plan helped me avoid some of the verbal fighting I would have had to do otherwise. I think that having things written down and signed says, "I am damned serious about this and I WILL make a stink about it." That's enough to make at least SOME folks glance at the plan before walking into your room.
Probably the most important reason to write a birth plan is that it gives you an opportunity to discuss your preferences with your HCP ahead of time and find out what items might be an issue. For example, I had "wait up to 1 hour for placenta to deliver naturally" on mine this time, and my MW said, "I really can't wait 1 hour, but 30 minutes is reasonable for expectant management," so I listened to her and changed it. It's helpful for me to know that ahead of time, so I don't get angry with her in the moment for what I perceive to be "active management" on her part. KWIM? It's good to know where they feel they really can/cannot compromise for legality reasons, safety, etc.
A good HCP will also give you some advice about how to advocate for yourself with the rest of the hospital staff. For example, I put on my birth plan "in case of C/S, if DH must leave with the baby, please allow a second support person inside to accompany me." My MW told me that this doc is ok with a 'doula' stepping in, but might balk at having my mother come in (for example), so I should just call her my "doula" and it would be fine. This is very good information to have ahead of time. I can think of lots of examples where my HCP's have given this kind of advice based on what I wrote in my birth plans.
I think that birth plans can cause hostility or amusement when they are a little ludicrous -- like the person who writes "No IV" on her plan but right below it says "I want an epidural." Obviously she has no idea what she's doing with that birth plan, because one cannot get an epidural without IV fluids. Others put things on the birth plan that are outdated or show a lack of information about the hospital. Writing "please do not shave my pubic hair" is probably unnecessary at most hospitals these days, for example (though it's not completely unheard of). Likewise, if nobody in your HCP's practice does routine episiotomies, you can probably leave it off your birth plan, but if you know that some of them are a bit scissor-happy, you might want to make a strong point of saying DO NOT CUT ME on your birth plan. A well-written, respectful, clear, concise birth plan that stays away from outdated, silly or outrageous requests, though, should really not be met with ridicule.
It reminds me a little of the contracts that performing artists send ahead for their gigs -- most of them have a section for personal requests, and most of them are perfectly reasonable (i.e., "please have 5 bottles of water available backstage and a private area to change clothing"), but some are totally ridiculous ("three bowls of yellow M&M's to be waiting for us in our dressing room when we arrive at 2 am"). The ridiculous ones cause a great deal of eye-rolling and annoyance among staff at the concert venue (especially when you're the chosen M&M sorter), but really, they don't raise eyebrows, otherwise.
Now, I'm fortunate to have a lot of hospital choices in my area (you might not have those sorts of options), but I chose my birth hospital this time specifically based on the nurses' responses to the question "do you recommend bringing a birth plan?" If they say something like, "the longer the birth plan the more likely the C/S," (which I heard at hospital #1) or "well, come with ideas of what you want, but don't write it down and tape it to the wall or anything" (which I heard at hospital #2), I keep looking until I find a more supportive environment. The hospital I chose makes a strong point of encouraging written birth plans from every woman who walks into L&D.
I see the birth plan as an extra layer of insurance -- alone, a birth plan is not enough, but combined with strong verbal self-advocacy from you and your partner, AND a HCP who knows your preferences and has agreed to honor them, AND a hospital with reasonable policies and procedures, it means you're pretty likely to get the birth experience you're hoping for.