Most people who don't shamelessly self-identify as "casual" gamers dislike randomness in games, but a lot still think that a small amount of it can be a good thing. That actually makes me really mad because it's obvious that randomness inherently punishes players for decisions that were actually optimal given their information and therefore is inherently unfair; scaling down the degree doesn't change its nature. And all of the argued benefits of randomness are at best things you don't need randomness to get.
One of the most obvious arguments people make for RNG is that it helps keeps every match fresh. However, games like Dominion and Prismata and even Chess960 well refute the idea that RNG is necessary for this, or even that it's hard to achieve it without.
The RNG argument: "in a completely deterministic game, skill is skill, and so if you're even a little bit more skilled than someone else you'll win nearly all the time. It'll be almost impossible to find opponents you can have a balanced winrate against".
Prismata obviously is the perfect counterexample. This is a deterministic pure strategy game with no hidden information or any other "RNG by another name" mechanics, and it has extremely high performance variance. From my experience as a near top player in Prismata I'd say a 200 elo advantage is something like a 70% winrate. I never felt like I could autopilot when playing against someone even 500 points below me, because every time I did that I lost.
I still don't have a ton of insight on how to create performance variance in a fair game, but Prismata shows that it's absolutely possible.
The excitement of uncertainty.
There's also an occasionally raised argument that randomness is actually enjoyable. It tends to go something like, "uncertainty is essential for engagement; if you know what's going to happen it can never be exciting". This seems a very similar fallacy to the argument some people make for persistent consequences for failure in singleplayer games: presenting a false idea of how fun works and not bothering to even check it against one's own experience. The "excitement" of playing games comes from two main emotions: engagement, which is triggered by the exertion of effort; and exhilaration, which is triggered by making important decisions. There's no enjoyment of having your fate affected by something you can't see and can't control. That type of "uncertainty" in fact stresses us out because due to loss aversion we usually feel the negative possibility much stronger than the positive possibility.
I should mention here (maybe I'll move this to a separate article but not for now) that by far the most exhilarating game I've ever played is the deterministic perfect-information (and turn-based!) Go. Go doesn't need any crap like "the excitement of uncertainty"; it has the excitement of heart-pounding tactical decisions with the lives of entire groups riding on them.
I've never seen a person who treats games as wholesome competition and doesn't demonstrably feel upset at randomness in them. But bro I've been a competitive player of many games. I have played games with RNG and enjoyed them for their other upsides. Not once have I ever experienced any effect like "the excitement of drawing a unknown card".
I think the fake idea might stem from an attribution error: it might be that people think this exists because they know it feels good to have RNGesus favor you, and they falsely attribute that to RNG being enjoyable when it's actually just the enjoyment of winning; and when they feel the dissatisfaction of RNGesus smiting you, they falsely attribute it to just losing in general being disappointing.
I don't remember hearing this argument raised recently, but I know I've heard it before. The argument is "randomness gives players a chance to come back after a mistake. This keeps the whole game interesting instead of making it get stale as soon as someone takes a significant lead".
This one is really ironic because this is actually a problem mostly created by randomness. Something exists called resignation which is the real solution to being behind; the only reason this argument even gets raised is because of games where you feel you can't resign because you still have a tiny chance of winning. This problem is, obviously, exacerbated by randomness. I used to play a CCG called Spellweaver with a lot of randomness, and I had loads of experiences where I knew I was behind and I was no longer enjoying the game, but I couldn't resign because there was that one card I knew was in my deck that could turn around the game if I drew it; I had to hang on until the bitter end incase that happened even though I knew it was unlikely. It was actually the randomness that was causing my misery. When I fell hopelessly behind in Go or Prismata I always just resigned and I was never dissatisfied beyond the inherent dissatisfaction of losing.
It's also not at all impossible to have a deterministic and fair game where comebacks are possible and commonplace. In fact strategy games are really the only ones that commonly suffer from this problem at all. Fighting games usually have comebacks be a very frequent occurrence even without any randomness. I discuss comebacks more in my page on feedback loops.
This might be surprising, but there's actually a pretty understandable case to be made that randomness helps make games deeper. Making the right decision a matter of probability often makes it far harder to know what the right decision is; Spellweaver was actually a good example of this. A lot of common situations existed where the decision depended on what cards you wanted to assume the enemy might have, and so you could never really prove what the optimal decision was. Top players disagreed. And when I tried to create my own CCG for a while, I learned the hard way that removing hidden information, in an attempt to make the game more deterministic and fair, actually trivialized most of the decisions in Spellweaver and it just came down to deck matchups or draw RNG.
But this doesn't mean that randomness is in any way necessary to create a sufficiently deep game, just that it can be one way to slap a bandaid on an otherwise dreadfully shallow game. The deepest game in the world is still Go as far as I'm concerned. And by orders of magnitude. So this doesn't make randomness a good thing or even a necessary evil, just a crutch that can cover for some of the weaknesses of an uninspired design by replacing it with other problems.
So no, randomness is not okay, and yes, it's possible to make a game with no randomness at all and still has enormous depth, variety of experience, uncertain outcomes in unequal matches, is extremely "exciting" to play, and doesn't bore the losing player.