NFP has a perfect use rate (and similar typical use rate) the same as the pill *IF* the user has been properly trained and knows what to look for AND follows all the rules. Granted, there are various methods out there and I truly wouldn't put much stock at all in the ones that rely only on temperature or calendar calculations. However, the ones that rely on cervical mucus (Billings and Creighton); a combination of cervical mucus, temperature, and cervical postion (Couple-to-couple league, CCL, or sympto-thermal method, STM); or cervical mucus, temperatures, and an ovulation meter (Marquette) are all backed by science and have very high efficacy rates. All of those (depending upon the study) have efficacy rates at 98-99.9%--which is on par with the pill.
NFP isn't always easy, particularly when you're first getting started. That's why it's ideal to have an in-person teacher who can guide you and answer your questions and clear up any misunderstandings. (There are some home-study kits and online communications for those who can't find a close teacher.) However, once you know what you're doing, it doesn't matter if you have regular cycles, highly irregular cycles (even PCOS) or are breastfeeding--you can learn how to interpret your body's fertility and plan your activity accordingly (whether you want to avoid or get pregnant).
Learning how to read your body's signs is a little more difficult than remembering to pop a pill at the same time everyday or use a condom or have an IUD inserted, but there are also no side effects and, once you've been trained, the cost is minimal to nothing. Furthermore, since you're paying attention to your body daily, you can often detect when something is wrong and get it fixed sooner.
You're right--there are no guarantees that every cycle is the same, but if you're using one of the above mentioned methods, it doesn't matter. And, there are also no guarantees that ANY birth control method is going to work 100% of the time either. I can name people who conceived while they were on the pill, or using condoms or had an IUD......even sterilizations have a failure rate.