Ahri gets more than 5 casts. Natural regen, dorans regen, and killing minions. Mana management is a thing, all mana users must adhere by it. Mages are only gated by CDs until mana hits 0. Same with Zed and energy, but he hits 0 far quicker. Sure it comes back, but he has windows of vulnerability much more frequently than a mage who can keep up an assault until mana hits 0.
22s CD is not meaningless. This is purely bias, subjective rhetoric. This game is not balanced around Bronze solo q. It's high plat+. 22 seconds is massive, and junglers do identify this window and gank. I don't know about your games, but it happens in mine. Also, it's meaningful counterplay. He gets a poke ranging from very little to colossal damage (Depends on your positioning) every 22 seconds. Riot gave the counterplay, if the players don't take it, it isn't their or Zed's fault. It's not free damage, it's completely CD and heavily so gated.
You don't counter harass a 1400 max range Q. You don't get hit by a 1400 range Q. You're providing a ridiculous scenario in which you're just pumping up various strengths in a hyperbolic way. Yes, his Q is 1400 range. That is a 22 second CD, loss of mobility, and a long travel time along with possibly passing through a unit and dealing half damage. Also half the energy is gone. You harass when he CSs. He goes in (Remember, he's melee) and you Q. Simple. Or even auto.
You can Q more than 6 times in a lane. I don't know where your mana goes. Don't spam, land spells. Zed can "Spam" but each spam is relatively low in damage. Unless a full W-Q-Q-E combo hits you, you don't take much damage. Especially with the nerfed Q going through anything. Your jungler enver stops by, that's no fact. That's a personal experience in a game. My jungler stops by, we kill Zed. Their jungler stops by, they kill me (As Zed) when W is down.
Zed can miss all the time, sure. He has no max resource to deplete in the sense mana does. However, his Q does less than yours unless possibly he hits you directly which isn't too easy in lane since if there's a clear path between Ahri and Zed, there's a clear path for charm. His Q does heavily reduced damage, yours is an amazing wave clear.
Zed is imbalanced early game, this is true. Why? Late game he is weak. He gained late game power due to QSS removal and nerfing of Zhonya so it isnt staple on anything with an AP scaling, however he lost 4 seconds on rank 1 W and lost AD ratio and base damage on Q. So they balanced his power out a bit, and that's why in lane he's weaker than before and late game he can still try and be relevant. Champions are designed this way. They typically have power spikes early, mid or late game. It's just the early game powerhouses are hated due to the efficiency of damage early levels. No Mundo has fun getting popped by Zed's ult early game, but no Mundo puts down his bag of popcorn as Zed's ult tickles late game.
Your comparing two champions unfairly to each other with a victim complex. "Ahri cant do this this or this, Zed can do this this and this.
Here's bare bones what both kits offer and maybe this will help you see balance, or at least allow others scanning your comments not to be simply fooled and run around banning Zed.
Zed: Mostly AD damage, passive is magic but not enough to warrant factoring in resistance wise. Long CD mobility spell that doubles as harass. Energy based, high damage. Ult requires large set up time. Hardly any CC (Only slow is on that 22 second CD). Some people consider Zed's ult a mobility spell. It's situationaly mobile. Need to hop a wall? It doesn't simply do that. Need to get to lane faster? Doesn't do that. Side step a skill shot? Doesn't do that. Catch up to someone, it can kind of do that should you be in range. Can sidestep a skillshot by ulting someone, but that's a full commitment which might not be an option. Melee based, has a ranged poke that severely cuts damage should it hit anything first. Can get in and out pretty easily with use of shadows. Good AOE.
Ahri: Full AP assassin/mage, no AD aside from autos. Has sustain, hard CC and true damage. Extreme mobility in the form of a triple dash ult requiring no lock on and a speed boost upon using Q. However, as mobility is on an ult, less opportunities to be mobile, but better when doing so. Mobility also deals great damage. Ranged, mana dependent. Heavily skill shot oriented, but like champs like Panth, has a guaranteed combo should CC land. Great AOE, can get in and out with ult easily.
They're both great champs, but they do different things and hold different strengths and weaknesses.
Here's the biggest problem you seem to have. Zed's Q. You see it as a resourceless, easily hit skillshot that chunks and does so much for Zed. I see why you see that. Now compare Ahri and Zed's Qs.
Zed: Linear pass-through skill shot costing about 25-33% energy. Physical damage. Can have extended range every so often.
Ahri: Linear pass-through skill shot costing up to 85 mana, no percentages involved due to a logically infinite mana pool. Not saying it's better than energy, I just can't assign a direct percentage since mana isn't fixed. Deals magic and TRUE damage, provides a speed boost and provides sustain.
Now see this? Zed's Q is only damage. Itemizable-against damage. It has 0 other purpose. Ahri's Q provides utility, sustain and damage that can't be fully itemized against. This is why Zed gets more Q's than ahri. It's why it's faster and more direct. It's simply damage, and often even less than Ahri's. While Zed loses damage for multiple targets hit, Ahri charges passive and possibly heals MORE for more targets hit, all while everyone takes equal damage and Ahri gets a speed boost. So yes, Ahri has to manage mana, and maybe aim a little more carefully and decide when the best time to Q is while Zed can theoretically just press Q when off CD and not care (Ignoring lane shoving and how devastating that can be.) So while Zed gets this "Free ride" Q, it only does some damage. Ahri has to be careful with hers, but it heals, hurts and speeds up. It's also a more active zone, but that's a subjective thought from me. Zed's Q does some damage but if behind creeps, it will do a sliver. If Ahri's hits you, you get chunked hard due to true damage. This makes her Q more dangerous and makes it so she zones much better.
Ahri's Q is a standalone ability. It does what it does and that's it with very little synergy with the rest of the kit aside from the little speed boost. Zed's Q is a synergy ability that increases the damage his R does and makes his W have more utility with the possibility of many Qs.
But your problem seems to be early game and Q spam, that which isn't factored as much with the synergy. So until ult comes, Ahri and Zed have stand alone Qs, both functioning differently and paying prices relative to the power they're given from it.