The problem with that logic though is that there are a finite number of ways to generate probability when it comes to games. Eventually you have to repeat or it becomes tedious.
Roll dx
Roll 2dx
Roll 3dx
Roll 4dx
Roll (and you see the progression)
Alternative styles such as roll and keep, percentile, dx+dy, draw a card, draw a card from a bigger deck, and so on, cover that gambit but eventually they would expound to an unmanageable level.
It is clearly true that different ways of generating a random result are limited, and that they represent a fairly bland difference between RPG systems, but generation of random results is only a (rather small)
part of an RPG system. If you conflate "system" with "randomisation method" I think you are missing a world of variation.
Arguably the biggest differentiator between systems is "what are you rolling for?"
Are you rolling to see if an action succeeds? Or are you rolling to decide who wins a conflict? Or are you rolling to determine which player's vision of the outcome is taken to actually happen in the game world?
Another key system element is "how do characters change and/or develop?"
Do they get ever stronger at combat? Do they change their passions and goals? Do they change at all*?
Considerations like these will alter radically the way the games play out - regardless what randomisation tools are selected to generate the random outcomes.
*: In Classic Traveller characters didn't change mechanically after character generation at all - unless they died...
One point that I don't think has yet been raised is that it is only complexity which allows diversity. At the maximum end of simplicity, all systems are exactly alike: The GM decides what happens.
a) Why does it have to be the GM? Games like Primetime Adventures and Universalis achieve diversity by having simple mechanical systems that determine
who gets to decide the details of an outcome, and
how they are constrained when they do so (e.g. who 'won').
b) What is 'simple' about the human brain? It's the most complex and capable computer we know of by a fair margin (closest runners up being brains of other apes, I'd guess). Just because a system isn't written down doesn't mean that decisions aren't "systematic" - the individual doing the deciding is just making up the system as they play. The biggest downside of this tends to be that the system is not
shared or communicated effectively among the players.
In the end, I think I see what you are driving at , but you miss a 'layer'. To have a diversely engaging game you need not only subtlety/complexity of adjudication, you also need shared understanding and communication of that subtlety of adjudication - and that will tend to make the communication load quite heavy. One way to lighten that load during actual play is to have complex and detailed rules systems that can be read before play begins. It works, but it's not the only way to handle the communication load.
I would maybe argue that it's vital to understand how you are handling the comms load for any RPG you run, because otherwise you risk doing something that you imagine to be shared which actually isn't. My nightmare scenario is the GM sat there making subtle and intriguing decisions based on firm game concepts while the players make random decisions and get increasingly bored since they are not privy to any of this wonderful stuff and just see a bunch of arbitrary outcomes that they don't understand.