I play Warwick and Twisted Fate, and it's not hard for me to dodge cards. Devote more of your attention to it and anticipate when he'll throw and you'll do fine.

Hint: Most twisted fates are terrible and spam on cooldown at the place you were standing.

Morgana's shield is really ridiculous. It's not stupid OP, but it definitely needs to be toned down. Possibly just absorb damage instead of disable effects as well.

Edit: On Ryze, it doesn't matter if you take him as a team. If it's four of you vs him, yah you won't get one shot but he'll probably get a double kill. Now, if it's five of you vs him and two team mates he pretty much forces your team into BS situations. Stay spread out? Evelynn and Twitch pop on a squishy and kill them before you know what happens. Stick together? Better hope he's the only AoE or you have magic resist. That or have SVU on speed dial because you'll need it.

Pick on Ryze more. You have to keep him in check. He's squishy as hell and easy to gank with a little coordination. If you have 4 team members on him and he doesn't just get turned into a thin, red paste immediately then you let him farm way too much or someone on your team has been feeding him all game. He shouldn't ever be tough to kill AND still be ultra-lethal.

If 4 of anyone is required to counter 1 of anyone (assuming decent gameplay from both teams), it's a problem in my opinion.

But like I said, I don't think that's the problem.
The problem is more like 4 of anyone will have decent enough difficulty against evelynn and rhyze that it warrants concern, for example.

Ryze is definitely the best nuker in the game. Although he can come out with a ton of burst damage, he is fragile enough to be killed without much effort.

Although, it is annoying to see noob players getting kills because of his ridiculous damage output.

I hate Amumu hands down. It takes 3-4 people all armed with stuns to get him down...

Best raw burst nuking yes. Best nuker/dps caster there is a ton of competition. Annie is an extremely good nuker as well as karthas who is arguably the best of the 3 (though he is certainly one of the more difficult champions to play so I dont think you will see as many people being dominant with him in lower brackets.)

Banshee veil > Ryze btw

Hero that can push a lane alone for instant Twist is a bit overwhelming. You can't stop him from farming nor can you really harass him. Ryze is just a hero killer, not that good at pushing early game nor mid if he was not fed. I don't mine hero killers as much as a hero that can lead a team single handily in pushing a lane down.

Hmm. I've played approx. 60+ games and random hero selection about 30+ and I haven't really notice any OP heroes yet. Twist - you can just dodge his cards and if he tele to heal then push that lane hard. Ryze - boost spell / flash works great and you can also get armor against it. Amumu - boost and lifesteal crit gear. So from what i've seen there's a counter for everyone. Just adapt to who your playing against and you should be fine.