Riven does not need nerfs, she is not OP, and she is not problematic
While I am fully aware that there are weaknesses in my argument, I am sticking to it since there are weaknesses in any argument; nothing is perfect.
My first examination is her winrates across all levels of ranked play. Lolking's stats for Riven show that she has a steady winrate in the aggregate even within a small sample of 26 days. She has the second most stable winrate in bronze and then silver. Gold+, and especially in Master+, shows erratic behavior. Since Bronze + silver makes up roughly 80% of the playerbase and therefore gold+ makes up the remaining 20%, this suggests that spikes in her winrate are simply artifacts of randomness.
Artifacts of data happen very frequently. When we think of randomness in the long run, we tend to think of the uniform distribution PDF: a flat, horizontal line. This is indeed what we see in the aggregate but not in the top 20%. Her non exclusive pickrate from LolSkill is 18%, which is by no means small. It's enormous. However, since non-exclusive pickrates are never in a vacuum, we must consider that people are picking her for reasons (due to perception) outside of a perception that she is powerful.
If we look again at LoLSkill's matchup page for Riven top, we see that she has a biased spread of matchups. Out of 45 matchups recorded, 16 of them are unfavorable and 29 are favorable. Her winrate clearly shows that she is statistically more likely to win barring other information. However, we can also see that there are plenty of other tops people would agree as normal picks that beat Riven.
The perception of her power stems from the above, but she loses to top that are flat out better than her in overall winrates e.g. Heimerdinger (52.3%), Wukong (54.1%), and Tryndamere (53.4%) vs Riven's 50.8%. We can also rule out what I would call "conditional picking" due to her absurdly high pickrate of 18%. Conditional Picking would apply to champions who are picked in a very specific circumstance, which would skew the data as not being entirely independent, where picking a particular champion in ranked, such as Yorick, inherently suggests that there is something different about this game. However, if Riven is a conditional pick, she is being picked so much that her condition to do well is an accurate representation of the game as a whole. As such, we could still treat her being picked as independent of the situation as there is nothing special going on.
Therefore, I argue that Riven does not need the nerfbat due to performance. This is part 1.
Part 2 is nerfs due to her playstyle. Riven is a snowbally champion. ADC snowball, but their snowball mechanics require them to be in a very good position so they don't get blown up as well as being unreliable. 30% crit is unreliable, and attack speed isn't useful if you're constantly moving and unable to get off shots. Riven gets a reliable damage multiplication that depends on a single stat source as opposed to three. Thus, Riven's play tends to be unforgiving . Second, her multiplying stat not only gives her sustain but also burst durability in the form of her shield. Building pure AD on her, while unadvised, is most definitely more effective than full AD on Xin, Yi, or even Pantheon or Talon. It's more effective than Kha, and playing Riven who has snowballed is arguably more forgiving in nature than a Zed, Rengar, or Yasuo who is also fed. These three rely on skill mechanics (displacement, stealth, and a windwall) as opposed to simply getting survivability for being. Regardless of how easy you may think it is to pull off a decent ult as Zed, Rengar, or press W as Yasuo, Riven just has to press E, and she would still do it simply to move around and go places. The presence of Riven's shield changes little about her decision making when using E. There are few instances where you would give up the ability to move out of range in order to absorb a spell as Riven. They exist, but they are few as it compounds problems instead of just getting out of there.
Therefore, we combine these two pieces to get a champion who is unforgiving to play against and forgiving to play as to get Riven. The main problem with that conclusion is that she does not have a Certain(ly)ty in her zone control. That does not mean she is ineffective in it. It just means it's not as reliable as Malzahar's who can hit you with 4 spells within 0.5 seconds purely because 1 is area, 2 are targeted, and the third is ridiculously easy to hit when you are a sitting duck. All of Riven's spells are skillshots. She still has to aim her QER, and she can use W and not hit you. A solution to combat her would be to choose champions who have certainty in their zone control. The main weakness of these kinds of champions is their low range. Riven is melee, and so this doesn't apply. Another solution would be to simply outRiven Riven by choosing a champion who simply overwhelms people in durability, sustain, and early presence. One way to do that would be a mirror match, but another way would be to take the playstyle of Riven and find champion that have similar styles but are more certainty (e.g. Garen or Wukong, who both have certainty in their main way to get to a target and then followup with either Garen-teed damage or extremely easy to hit damage when in range.)
But those are tips of who to pick. Let's say you pick Pantheon vs Riven. Well, Riven statistically does well vs Pantheon. I played Pantheon religiously in Season 4, and played against a multitude of Rivens. The only real thing that was almost always hard was the game of chicken with my Q vs her E. Everything else was simply adjusting my playstyle to deal with a very snowbally champion and more about minimizing my mistakes than trying to get ahead. There are plenty of champions you can make mistakes against and be perfectly fine with virtually no change in chance of winning. Riven is not one of those champions.
So Riven is unfun to play against probably because she forces a burden onto other players instead of having the proverbial dance in lane. The main problem with nerfing her because of that is she is very one-dimensional in what she brings to the team. And that is ok. Riot is not reworking champions because everyone needs to have some minigame like Fiora or Skarner. They are reworking them because it's not fun for a lot of people to sum up 33% of the roster with "passive is free stats, Q is a nuke with light utility, W is some form of heavy utility damage, E is more focused on defense, and R is the 'nuke them to hell' button. W and E can be swapped if necessary." It's ok for a handful of champions to be like that, but not a huge portion.
So why leave Riven instead of say Garen? It's mostly on a case by case. In Garen's case it's because he's supposed to be the Noobtube of League. He should be very easy to play with a lot of effectiveness. Currently, he's not the latter. For Morde's case, Morde has historically been Yorick levels of unfun, so Riot wants to make him more viable while making him more fun to play as but more importantly to play against. But for the main reason why I think Riven should not be nerfed, she is the next step up from Garen. She gives more power than Garen and is more specialized, but is significantly harder to play. Let's be honest; a bad Riven is much less effective than a bad Garen.
So, for a Tl;DR, I'm sorry to say it like this but... git gud.