Nobody said don't play ranked with Riven, in fact throughout Season 4 I played her consistently in mid, top and jungle because she has an amazing kit.
Her squishiness is never a reason not to play.
+ every other assasin, marksman, and AP carry are common to find played in every tier of play, and more than effectively)
Animation cancelling will have absolutely nothing to do with surviving team fights - that comes from learning her kit and knowing when you can and can't engage to maximize survival potential. Squishiness is also entirely relative to your build. Riven's also an extremely good splitpusher with her passive combined with her Q + Tiamat active, meaning you may not be in every single team fight.
Where I suggest you start learning: proper Creep score. As much as you may think it doesn't matter, it seriously does. It makes a MASSIVE difference. Let's assume you miss two minions per wave at 19g each (38g/30 seconds)- in the first 6 minutes of the actual laning phase, you've given up more than a kill worth of gold - most players in bronze-silver miss an average of 2-3 per wave, every wave. That's a massive gold difference.
Another place to start: Learning different lanes proper aggressors. Some lanes have rightful aggressors and pacifists, meaning the aggressor is going to walk all over you if you engage before you get your own powerspike. Example: J4 vs Riven - J4 has a level 2 powerspike and good kill potential, Riven's comes at 3. Your job as riven in this lane is to survive until 3 and punish him with your insane amount of CC and mobility along with your self-shield from E. Every lane has proper aggressors and pacifists, and you have to understand where you sit in every lane.
Another place, understanding how to win a lane before the second wave.
Another, understanding gold balance.
Another, getting used to proper warding patterns and map awareness (this is absolutely huge, I cannot stress this particular point enough) The average bronze player finds and clears 1 vision/"pink" ward throughout the game and 0 sight/yellow wards before they expire. In comparison, your pink ward in an average high Diamond match is expected to last less than 7 minutes, and your sight ward is expected to last less than it's full duration - that averages less than dragon respawn based on how often you lay a pink vs a sight ward.
Another great thing to learn, proxy farming.
Another absolutely massive one; decision making.
I could go on and on and on, but I won't. The point is, animation canceling is something that a lot of low-mid diamond level players are still mastering. It doesn't come easy and won't make a huge difference in your game, especially when playing a champ like Riven who is more reliant on her CDs than AAs in team fights (Before anyone pipes up with a "holier than thou" attitude; yes, I'm aware her AAs also play a big part in her potential due to her passive and basic trading technique, same with Darius)
Master the big bits, work toward the smaller ones. Invest some time into spectating some of the games on the home page, they're usually featuring high diamond/master/challenger level matches. Yes, it is an investment. It can show you some of the things you're doing wrong by watching someone else make the same or a similar mistake and having their opponent capitalize on it - that usually results in a death.
(On the note of death, try to get away from the notion that a death is only a lost trade/gain of 300g to an opponent - it'll help you stop making silly trades time and time again, ending up with feeding because it's so much more than just a 300g boost to the enemy laner.)