I am currently prepping for my first contests (April and June) and have a coach, and I'm extremely thankful to have one.
-I don't have to obsess or over analyze everything I do as I have someone to guide me.
-If I AM obsessing or over analyzing something, I can bounce it off him and he'll give me the info I need, educating me in the process. Daily weight fluctuations, training issues or questions, aches and pains, calories, meal timing, posing, etc., anything and everything.
-As many have already mentioned, as the show approaches, especially the last couple weeks, day before, day of, you want the experience of a successful pro to guide you through the process. Water management, tanning, show logistics, etc.
It seems like you have a preconceived notion that all coaches want to do is get your money and give out generic advice, although you've never actually hired one. I think, as with any profession, it really depends on who you work with. There's no doubt some coaches aren't worth it, but there are also a lot of outstanding coaches that have great experience and can offer invaluable expertise.
When a coach says, "we'll see how you respond to X," it's because they don't know how you'll respond to X, as everyone is different. Making small changes is one very important aspect that is often overlooked, as some people go into "prep mode" and make a lot of drastic adjustments in a short amount of time, so there's no way to tell what exactly is effective and what needs to be adjusted. Small adjustments, consistency and data allow you to really gain serious knowledge.
As far as the "learning process" it seems silly to rob yourself of gains and success because you enjoy "figuring it out." These things don't need to be mutually exclusive, you can learn plenty working with a coach. I can tell you I have learned quite a lot about myself, my body, my training, nutrition, etc. through working with my coach. You don't want a coach that says, "do this, do whatever I say, don't question and just get it done," or that sends you adjustments or a plan without explanation. You want a coach that you know you can talk to, that will educate you and provide the method to the madness, not just the madness.
It might be a good idea to stop thinking about popularity of a coach and politics and such, and just find a coach who is experienced, who has had success as a competitor, has had clients that look great for their shows (don't focus on clients who win or place or whatever, this is an offense only sport. If the clients look good, you know the guy knows his stuff), someone who's a nice guy and isn't so busy that they can't answer your questions in a timely manner.
Hope it works out for you, any shows coming up soon you're thinking about?