The limbs are not meant to be followed in a specific order; however it is important to note that the original writing didn’t go into specifics or depth. Instead the original text left each person to their own interpretation of each string.
Furthermore focusing on a single limb does not mean to disregard the others. A good example of this would be speaking truthfully (“satya”) however you want to do so in a manner that isn’t harmful (“ahimsa”). Using this example, we are able to re-examine a couple of the Yamas together at the same time.
Ultimately, the philosophical reasons for the Yamas and Niyamas are that if you aren’t considering them, you can’t possibly find a state of Samadhi. Therefore the practice of Yoga can not simply be a physical one.