I was coming here to read and see if this was actually good information, but the funny thing is none of those guys you listed are purely stats let me explain.
champions who are considered just stat sticks are people with no meaningful decisions and little to no team utility. AKA Shyvana/darius/garen/fiora are good examples, but what you're saying is actually not what people use for the term stat balls.
Yi is a champion that no one ever wants to hear actually takes meaningful decisions because his skill floor is so low that its easy to succeed, but his Q and W have extemely meaningful decisions even if his R and E are just stats.
Udyr: This is a horrible example and leads me to believe again you misunderstand what the team "stat ball means" every cast he has is a meaningful decision on what he currently needs in his moment. tankiness? speed? burst? sustained? YES all of those just enhance your autos and effectively give you stats, but if that is the term you use then every single champion in the game is a "ball of stats" becuase thats exactly how abilities work, they enhance your killing or saving potential. His abilities dont just give him stats they affect how he and the enemy plays which is exactly what a champion does.(im not saying udyr doesnt have balance issues, but im disagreeing that what you are stating is the issue)
Trundle: This guy is the closest to anything you're talking about and to some extent I see that, but his gameplay is actually not just about being a ball of stats but directly to actaully TAKE stats from other people. He is in the game to drain and help weaken that frontline so your carries can tear through them. Pillar is also a very unique and extremely non-staty move.
Ryze and caitlyn are aslo not great examples because Ryze while not being hard to learn, takes strong micromanagement and is one of the harder champions to manage before you have cdr and in lane. And cait is just like any other adc, they "could" win a 5v1 just by right clicking if they're fed enough comparatively to the rest of the enemy and that is how they are designed and built.
I'll conclude by saying what you're talking about are champions with really low skill floors which means one can be awful and still succeed as that champion. While I agree they are never really "fun" to lose to the problem is they will always exsist and they HAVE to exist. Ive been playing this game for 4 years and im guessing you have for a while too, but you cannot forget that every single day there are people who are "new". Maybe they are new to mobas, maybe new to league, maybe just new to the mage/carry/assassin role, but a good game that is successful NEEDS champions who are relatively easy to play so that you can learn. And since riot designs their game to make every champion "viable"(just using this term not talking about competative viability, just what is considered playable) that means that there HAVE to be easy champions that can succeed.