It really depends on your skin. Some people can't tolerate "natural" skincare but some can. You've got to do what works best for your skin. There's no point going natural if your face is a mess because of it!
I find that the less junk I put on my face, the better. I cleanse with Natural Instinct (natural/organic australian brand) cream cleanser in the mornings and the oil cleansing method at night, and I moisturise with jojoba oil and my skin is looking really good. Prior to this I was using many products with AHAs to try to clear up my skin and although it worked very well, it plateaued after some time and I wasn't keen on using acids on my face forever, not to mention it's really high-maintenance and I couldn't be bothered.
If you don't carry those "chemical-free", pure, natural etc principles into what else you put on your body, what clothes you wear and what you eat and drink (and so on), then you might think going natural with just your skincare to be redundant. Personally I would find it very difficult to carry on a wholly "natural" lifestyle so I do what I can insofar as it works for me.