Well, I have run a search and the 2011 NIV now translates sarx as "flesh,"at least most of the time. Romans 7:5 now reads "When we were in the realm of the flesh". The idea of the "realm of the flesh"is still more than what the Greek says ("in the flesh"), but I think it does the job. It brings the reader closer to the original while using modern language, which is the goal of the NIV. I commend the translators for undoing a translation that has stood for 32 years and has been the source of confusing theology. I agree that sarx, is still hard to define and comprehend, but I think "flesh" is a better starting point than "sin nature".
But the title of this post also includes the word "mostly". I say this because in spite of translating many of the instances of sarx in Romans as "flesh", the translators have left two occurrences of "sin nature" behind. These appear in 7:18 where Paul famously tangles with the good he wants to do but does not, and in 7:25 where Paul declares that he is a slave to sin. In both of these verses it is still the "sinful nature" that causes Paul to act the way he does. And in these two cases I think the translators did not go far enough. I think they should finish the job and translate sarx as "flesh" here as well. I really not sure why they deiced this approach. This is what they have to say about sarx.
Especially in Paul, sarx can mean either part or all of the human body or the human being under the power of sin. In an effort to capture this latter sense of the word, the original NIV® often rendered sarx as "sinful nature." But this expression can mislead readers into thinking the human person is made up of various compartments, one of which is sarx, whereas the biblical writers' point is that humans can choose to yield themselves to a variety of influences or powers, one of which is the sin-producing sarx. The updated NIV® uses "flesh" as the translation in many places where it is important for readers to decide for themselves from the context whether one or both of these uses of sarx is present.
Again I commend them for their job. I just wish they had gone a little farther. If they want the reader to decide what the context is saying about sarx, then they should let the reader do just that.