Riven is a very safe and very snowball heavy champion, both of which do not mix. She really has no part of her design which isn't to her advantage other than being melee.
She is mono-scaling (scaling with a single stat is better than scaling with multiple)
She has short CDs with mobility
She is AD
She has survivability which increases with her damage
She has great power spikes
She, as you said, can snowball to become virtually unstoppable
Yes, she has counter pick options, so does every champion in league, but she has very few and far between, then even of those options, most do not have equal engagement, reliability, and stick, to off-set her mobility, burst and consistency.
BoxBox has shown (since her release more or less) that she is hands down game breaking in terms of reasonable counter play and reliability.
She is one of the champions that has perpetuated league into a more action RPG, than a strategy RPG with action mechanics. She is a champion who has a very difficult kit to take advantage of and a very easy champion to get return on knowing only her limits. (as in if learn riven well and only learn other champions second hand, you can still preform moderately well).