First, let's establish the timing. Here is a graph showing the frequency of the phrase in Google's digital library (Ngram). There are lone, infrequent examples from the '60s through the '80s -- as in, probably one reference a year, once every 5-10 years. It's not until 1993 that it begins a steady rise, though. Searching for the related phrase "random kindness" shows basically the same picture, only the out-of-the-blue rise begins in '92. "Acts of random kindness" explodes from out of nowhre in '94. Searching the NYT shows the first instance of "random acts of kindness" in '94, "random kindness" in '92, and "acts of random kindness" also in '92. Searching Amazon for books with "random acts of kindness" in the title shows that the earliest ones were published in '93.
What was it about the '92 to '94 period that led to the take-off of this movement? Evidently lots of people felt that there was a mismatch between the supply and need for kindness. As falling-crime times began, either folks grew stingier with kindness, or others were now in greater need as the society grew more antagonistic, or both. As recently as the 1980s, people were pretty friendly toward each other -- the low levels of shrill or harsh treatment meant that most people weren't in that great of a need for kind acts by others, and the relative lack of a glib and dismissive attitude meant that others were capable of pitching in when it was needed.
Obviously the movement did not reverse the trend, since social relations are even more fragmented now than 20 years ago -- hard as that may be to believe for folks who can still remember how sarcastic and apathetic the popular attitude had swung by 1994.
Still, did they at least pad the landing? It doesn't feel like it, not even during the movement's heyday in the later '90s or 2000s. Why not?
It wasn't simply the rarity of such acts. When they did happen, it wasn't appreciated by most of the recipients. If the performer overtly says that they're doing a random act of kindness, perhaps elaborating that it's part of a meta-goal to bring more happiness to the world, then the recipient feels like a charity case. Like they're just a tick mark moving some abstract quantity toward a quota. Even if the performer doesn't explicitly explain what they're doing and why, the utterly unusual nature of the act will tip the recipient off that they have some other goal in mind.
That brings up the suspicion of "ulterior motives." In friendlier times, the recipient wouldn't have thought much of the offer, but now that everyone's so hostile to each other, does this guy really want to be nice, or is he just trying to get something out of me? Like the "Free Hugs" thing -- clearly some outcast starved for physical attention who's trying to satisfy his need to touch girls, while dressing it up as altruism (if he has to hug the occasional dude, that's worth it to him).
It doesn't do much to elevate the performer either. Thoughtfulness should not be that thoughtful. The planned, deliberate, self-aware mindset that the performer takes on will lead away whatever other-minded intentions they may have had, and steer toward self-righteousness. And it doesn't do much to assuage their anxiety over how cold the world is growing, to believe that only calculated campaigns can keep relations friendly, rather than kindness spontaneously arising as needed. Finally, if there is an explicit goal in mind -- however fuzzy -- it sets them up for disappointment and burn-out when it, predictably, is not reached.
Beyond that, though, the most demoralizing part is the nagging doubts about how successful such a movement could be with everyone acting all isolated from each other. There doesn't need to be a national delegation, but even a local canned food drive or passing around the collection plate has a, well, collective atmosphere around it. It's not the kind of thing you can do all by yourself.
And the contact with the recipient seems too brief to sustain your motivation to continue. In practice, the performers took more of a stranger-oriented approach. Hold the door open for some old lady at the supermarket, wave a group of kids across the sidewalk instead of peeling out in front of them, and so on. But if they don't feel like members of your community, you don't get much satisfaction out of it. You don't get to see the enduring effects that you have on other people's lives because it's a one-off encounter. Nothing wrong with those drive-by forms of kindness, but they are the icing on the cake, and cannot substitute for friendliness among folks you know.
All of these factors explain why the movement arose when it did, but also why it's more or less burned out by now. Their heart was in the right place; it's just not an effective cure for the symptoms of anomie.
Historical precedents? Beats me. How would people 50 to 100 years from now learn about the "random acts of kindness" phenomenon of our times? It is something I can imagine the Pre-Raphaelites or other emo aesthetes taking a shot at during the Victorian era. Maybe during the mid-century, but maybe not -- they weren't as self-righteous as the Victorians or us.
Self-righteousness seems to show up during falling-crime, rising-inequality times. Widening inequality is marked by status contests among individuals, including do-gooders. Falling inequality, people aren't supposed to raise much of a hue and cry about things. Combine that with falling-crime / cocooning, and you get malaise, anomie, etc., but more of an Edward Hopper kind where no one makes an effort to help each other out. Though like I said, not like that appears to have much of an effect in our time.
At least people in the alienated mid-century didn't see themselves as targets for charity by deliberate do-gooders (from what little I can tell). That allows you to maintain more dignity through a period of social isolation. Performers of random acts of kindness only heighten your awareness of how unraveled the social fabric has become.