Low cost car washes are availble everywhere. It's the same here in Montreal (Canada). Around where I live, there are at least 6 hand wash car washes that charge around 6-10$ to wash a car. Despite that, I still have clients paying 200$-600$ to get services from me. So don't be discouraged by the low cost offer.
You have to look at detailing as a long term project. In the first few years you will not get that many client. The key is to make a good profit on each detail you do. Get your name out there and with time clients will come.
If you already master the detailing aspect, you might want to take a course in Marketing instead. Getting clients is the hard part of this profession, since you are targetting a very small part of the market (Rich people with nice cars who don't mind paying a lot more for proper care).