Before reading: A lot of things in League are debatable. I'm willing to discuss anything you may disagree with in my post.
He can dash in, outtrade you due to his passive, and dash out. This doesn't cost him any finite resource since he is manaless, and his cooldowns are very short so the frequency with which he can do this is oppressive
Well, yes, that's the point of his passive, so he can actually trade. Most melee champions have some AoE or long range skill shot for trading (Kass has his Q/E to trade; Katarina has her Q to poke; Zed has his Q/W/E combos to trade from afar) , Yasuo has neither of those besides his Tornado. Yasuo should only be going in for a trade when he has his shield. You're saying as if his shield is always up. It's not. You have time to out trade him when he's building up flow and you have a chance to pop his shield before he goes in for a trade.
-He can just constantly push your lane in, again without having to worry about managing a resource like mana
Learn to last hit under turret. Getting shoved into your turret is not a bad thing if you learn how CS while under turret. You can even still try to call for a gank, even if the chances aren't that great. While being shoved under turret is not ideal, you're making it sound as if you have to shove in order to win the lane.
A champion that can constantly shove lane, without costing any mana, and having all the mobility and outplay potential that he does (he can windwall my projectiles if he's mechanically good enough; i can't counterplay this no matter how good my mechanics are...he can tornado me to prevent me from gap closing onto him, and the animation is fast enough that i can't really prevent this)
Most Yasuo's are one-point-wonders with their W until they can't put points into their other abilities. This means in laning phase, the the windwall has a 26 second cooldown (24.7 seconds if he has 5% cdr in masteries). I can't think of a single champion whose ability to lead into a combo (stun/snare/etc) that has a 26 second cooldown. You have more than enough time to go in for a second go to land your abilities. Of course you can't counterplay something like that; it's about learning to bait out important cooldowns so you can try to trade with him fully.
The same can be said for his tornado. Learn to either bait it out engage right after he uses his tornado. He can't get his tornado back for another 16 seconds (15.2 seconds with 5% cdr). Besides, Yasuo will win a lot of the melee ranged matchups. Unless your a melee champion, you shouldn't be dashing directly towards him anyways. You'll want to keep your distance so he can't auto you.
Now, I don't like this kind of low-counterplay, unfun mechanic in the game...but you might be able to at least justify it if the champ's strength was being an early game powerhouse. But Yasuo is a hypercarry. This is due to his Doubled Crit chance and his innate armor pen - his damage scales higher than all but a handful of champs.
I'm not going to debate the level of fun since that's subjective, but it's short-thought to say he has low-counterplay. Yasuo has plenty of counterplay.
- Yasuo is melee. He has a harder time dealing with auto-attack harass from ranged champions (A majority of mid laners are ranged)
- Randuin's Omen works well against him. Reduced crit / reduced attack speed / more resistances
- You can still shove against him. Champions like Anivia/Ziggs/Azir once they get some mana regen.
- He's very reliant on fighting on minion waves. If he fights outside of his minions, he only has a single-dash on a 10-6 second per target cooldown. Unless he lands a tornado he's used up his gap closer for the next few seconds.
- Point and clicks suck for him. Vi, Annie, Kennen (kind of)/ Taric can all CC him well. Even if he windwalls the CC, his windwall is on a long cooldown.
- His ult can be QSS. His ult is a suspension and not a knock-up.
- His engages for trades are telegraphed well. Unless you're going into melee range to CS then he has to dash to a minion (or 2) to be able to dash onto you. If he dashes in a danger zone, you need to learn to back off.
- His crits are already reduced in damage.
- His ult only gives BONUS armor pen. You won't be affected by this if you're not building armor.
- Yasuo's Q is a skillshot. It's a short range and a short width skill. People can dodge his Q with practice.
- Here's a video explaining how to play against him
Not being gated by mana doesn't mean a whole lot unless you give a better reasoning why no mana is unfair. He's still gated by other limitations that manaless champions don't have.
-Yasuo has to be in your minion wave to shove the wave. This can only be done safely if the enemy has used their CC (so he doesn't get stuck in a wave and take minion damage)
- He has no decent ranged harass (Syndra has her balls; TF has Q/W/autos). A lot mana people don't have this issue.
-This means Yasuo's main way of trading is in melee range. Being in melee range is dangerous at some times. You may not be able to harass someone while under turret unless you join them under the tower; you may not be able react fast enough to a stun or snare.
- Unless he can get a good knock up while behind, Yasuo has no good way to get back into the game. Most assassins are feast or famine but a lot have some ways to do something to get back into the game (Katarina has a bunch of AoE to deal damage for assists; LeBlanc can provide some CC). The only way back in for Yasuo is to get assists (difficult unless in a 2v1 or got his tornado off) or to get kills (someone else far enough behind that his feast/famine playstyle doesn't matter or again in a 2v1).
A minor side note: Other champions also shove just as well as Yasuo and aren't using mana. Trist/Vlad/Morde/Riven can all shove the wave well without using mana (though Vlad/Morde use some health). I wouldn't say resource-less shoving is an unhealthy mechanic. A person could probably argue learning minion-wave control is unhealthy then since you can learn to shove with just changing how fast and where you've killed the enemy minions at.
My other suggestions is check your build path. He's going to start doing damage after his first item. Two key items against Yasuo would be seekers armgaurd (for laning phase, Zhonyas later) and Morellonomicon. You want the extra armor to avoid his burst and you want the grievous wounds since he builds lifesteal.