No, that's more true of DotA, and something that Riot (specifically Zileas) has said they want to avoid in LoL. Having a game be over at champ select due to hard counterpicks doesn't make for very interesting gameplay.
I guess I disagree that Zyra, in the redesign, would be as over powered if not counter picked as you claim. I think that maybe you'll have someone who specializes in Zyra so she gets banned, or she'll need slight re-turning, whether in design or AP ratio, in which case she'll also get banned. But honestly, looking at her kit, I don't see it being bad. Honestly, the main difference is her ult (which is a reasonable redesign regarding balance, especially since the old one was so strong in team fights). Honestly, I would expect that she's going to need reasonably high AP ratios to be viable.
Also, it's worth bearing in mind that he uses X everywhere instead of numbers- simply manipulating the numbers will play a huge part in the balance. It's impossible for many redesigns to figure how viable they will be. The point of the redesign was to address design flaws, not crunch numbers (correct me if I'm wrong author people).
Overall, I think games are at least as defined in champ select now as they would be with these changes. If you watch streams or even just play the game regardless, there are a fair number of games defined at champ select. It's not a majority, and I'm not accusing Riot of poor balance. I'm just saying- with 100+ champions, inevitable some team comps are going to be much stronger than others, and Riot has no power to determine who takes what champions and how much cooperation there is.