TLDR thesis: Between 1998 and 2008 anime had a golden age. This was, at least in part, due to a basic self-confidence in Japan's own ethos. Since then it has been watered down as further Western sensibilities percolate into their society, creating incoherent extremes of expression. The decrease in graphic nudity and violence is not directly responsible for a reduction in quality, but serves as a general indicator of what has transpired.
Detailed version: The reason this has been on my mind is because as I have been looking over my lists, trawling for new series, and generally contemplating the content of anime in recent years it jumped out at me that there seems to be an unusual surge of high quality in the late 90s and early-mid 00's. This has led me to wonder if anime did not experience a "golden age" during that time.
I want to be clear about what I mean by "golden age" so that my musings are not misunderstood. I do not mean that anime is going downhill, getting worse, or dying as we speak. Maybe it is, maybe it isn't, but that is irrelevant to my question. What I am focusing on is the idea that there was a temporary elevation in quality between the years ~1998 and ~2008 (porous estimate). I want to emphasize this because I am not claiming that old is good and new is bad. I am saying that, just like many other mediums in art, it had a heyday and that we are no longer in it. I also want to emphasize that I am not arguing nothing good has come out since ~2008. Clearly there has. I am focusing on the quantity of said productions.
I am confident that this is not out of nostalgia, for I didn't watch most of those series as they aired. I am only discovering them years later. Similarly, I don't think this can be accounted for purely by selection bias: that we remember the best and forget the worst as time goes on. This second statement is subjective, as it is based off a comparison of my scores for series pre-2008 and post-2008. I notice that all my 10s (technically S2 Mushishi is later) and a significant majority of my 9's come approximately 1998 to 2008. If it were just selection bias, I would expect to see an equal distribution through time of high-rated series, but a surge in low-rated ones in recent years. Again, yes, I'm aware this measurement method has significant weaknesses based on personal preference. But as you all know, I do have a high opinion of myself and have to express some confidence in my judgement.
So what does all this have to do with violence and nudity? If anything, given my usual standards one would think I would welcome such a reduction. My thought process is to wonder if part of the reason anime did well during this era was because it had a confidence in its own "culture." Japan has a strange culture that I do not pretend to fully understand. But what I do grasp of it, it seems to have an underlying ethos of sexual freedom/expression/naturalness that has not been entirely extinguished by the importation of Western values. Similarly, the depiction of true gore was not just for shock value, but again a more natural and realistic approach to what happens when people are grievously disfigured. This has naturally led many people in the West to consider anime excessively sexual and violent; whether this "excessive" is a fair judgement I will not say, but it did seem to be more in line with Japanese sensibilities.
However, in recent years these tendencies have gone underground. I can only speculate that this is due to a sort of further Westernization of the culture as the internet and true globalization have taken hold. Again, whether this is good or bad is another topic. But what is undeniable is that Western culture is itself riddled with inconsistencies, and when laid on top of another culture with its own idiosyncrasies it creates an incoherent mess. Showing massive amounts of blood pooling around a body is fine, but you'll be damned if you show even a hint of intestine. Similarly, have all the lascivious and stimulating sexual scenes you want, but a naked girl in a hot spring is a corrupting influence.
The problem this creates is two-fold in my view:
1) It suppresses their own aesthetic. It leads to an attempt to copy and please a standard which is not native, and so cannot be done with the same degree of elegance. It is imitation without comprehension.
2) It marginalizes the original tendencies, which puts them under a fetishistic pressure. That is, the culture still has that more flexible sensibility toward sex (I don't want to say "open", because I don't think that's accurate). However, when herded into a corner and denied proper expression for incomprehensible reasons, it tends to gush out luridly like a geyser. So rather than having casual nudity in anime, you have a tendency toward the squeaky clean (Western) coupled with a degenerate upwelling of the most revolting fanservice. I think this is less true for violence, but still noticeable that there now only crop up a few "graphic" series, and the rest have diluted their violence to be less shocking.
So in other words, there is a tendency to subconsciously please an alien aesthetic as well as an imbalance that leads to series being reflexively extreme in their depictions. It is overly-expressive and strangely omissive at the same time, but neither of these leads to true quality. It is notable that the few series I do mark as significant since 2008 (Psycho-Pass, Shinsekai Yori) are those that are at home with their graphic violence and open sexuality, respectively. This doesn't mean that sex and violence make quality, but that being at home with your own ethos does.
In summary, my speculation is that anime experienced a golden age of expression where several serendipitous elements came together, not the least among them a normal expression of Japanese culture. Given time this ethic was undermined by other influences, and anime lost its way trying to please a new and poorly understood sense of appropriateness. This caused it to lose some of its artistic and exploratory edge as it now found itself on uncertain artistic grounds, resulting in the production of safer, tamer, yet more extreme, series that we see today.
p.s. I must remark that I am not trying to account for every single change in anime production with this hypothesis. There are trends in the industry which are entirely separate, and which may be significantly more important. My goal is not to dismiss these. If anything, I think production methods have improved in many ways, such that today the anime industry is vastly more proficient at producing "refined trash", as opposed to the simple "trash" of yesteryear. However, this is a different topic and not one that I was focusing on with my musings.