1. You keep the board clear is nice in theory until you you play some games and find out that aggro decks usually outdraw control decks by a mile, hence they can produce multiple boards while you have limited and usually expensive removal. Also "No tech required against aggro" well, mate, your board clears are your tech against aggro. Think about it if there was no aggro at all, would you run low cost board clears in your deck and have them sit in your hand in mirror matches?
Comparing cards like Defile, School Spirits, Volcanic Potion, Brawl, Consecration, and Mass Hysteria - cards that are "widely ran" (just examples of AoE people might play, I don't usually play control) in control decks because AoE is generally good - to cards like Dirty Rat, Hecklebot, and Wild Bloodstinger(?) - extremely narrow tech choices that only function against OTK - doesn't really work. AoE isn't tech because it's versatile, you can use it in various ways to answer problems you're facing, sometimes against other control decks because Brawl and Mass Hysteria are that good. If weapon Rogue were popping off in Wild and somebody was running Kobold Stickyfinger as tech against it, that card would be useless against non-weapon decks.
What I'm saying here is that "tech" cards have an opportunity cost in building your deck, because you're sacrificing a slot or two in your deck for a card that's useful against a tiny portion of decks and useless against all the other ones. AoE isn't tech because it's useful far, far more often than any individual tech card is. The opportunity cost is so much lower.
2. On the no recovery - if you use tech card and pull/kill a combo piece OR APM mage doesn't kill you on in one turn there is no recovery in 99% of cases.
If a tech card works as intended, it still only eliminates 1 Flamewaker or 1 Sorcerer's Apprentice. A single Flamewaker and a single Sorcerer's Apprentice is all the deck needs to combo off and set up a winning game state. I've been a victim to it countless times. I've had Mages pop off turn 5 and fail to kill me, only to just play their second copies of those two minions and kill me two turns later. Fundamentally you're right, if you use all 4 of your pieces, fail to kill the opponent, and then lose because your pieces die, yeah I can't see how you'd come back from that. But that's not how people play the deck, so that fact is rarely ever relevant.
TL:DR flamewaker mage is no different than most aggro decks, has much higher skill cap, more easily counterable and can gas out.
I don't really agree with this take. You can play against aggro in a way that makes sense, and is possible without specific tech. You keep the board clear. You manage your health as efficiently as you can. Those are the things you do against aggro.
But against APM Mage there's no way to do either of those. They don't play minions. Unless you're a Warrior, your health isn't going above 30, which is a totally manageable number for the deck to burn away at turn 5-6. Playing aggressively to take them out before turn 5-6 is the only way to beat them, which isn't how you counter aggro - because that's how you counter a combo deck. But a regular combo deck would need to reach 10 mana (give or take a bit) to combo off, even then they'd need some level of prep.
I don't know what you're saying with this whole "there's no recovery" thing, the deck is like 75% spells that generate more spells, either by drawing them or randomly generating them. It has either 3/4 minions depending on whichever variant of APM Mage you're playing so Refreshing Spring Water nearly always is free or plusses you on mana. Sure, the deck can burnout to like 5 cards after 1 Flamewaker turn and still not kill you (anecdotally I had 2 full boards as even Paladin that Flamewaker Mage managed to burn through and kill me with anyway, so going wide didn't help at all) but if they keep a Flamewaker in hand they can still go again next turn and clean up.
And the "a God Hand is required for the deck to win" argument doesn't really hold up to scrutiny. If the deck was purely highroll, then why is it the most popular deck on Wild Ladder? Why is it doing so well if it only does well when you're lucky? Is every APM Mage just like, the luckiest person in the game? Sure, I've won maybe 2 games against APM Mage, but only because they were really UNlucky. If an absolute terrible brick-hand is the only game state where APM Mage can lose, it's not exactly "God Hand required" - it's more like "literally anything but the worst possible hand required".
I feel like there's a fundamental issue with the whole class tbh. It seems (though this might not be empirically true) that with each new expansion Mage in Wild gets an entirely new OTK deck, or one that's already frustratingly powerful is made all the stronger. The immense amounts of mana cheat, free damage, and stall. It's not really any single cards fault. The whole class is mechanically structured for this kind of stuff to be what it does.
It is pretty frustrating. It especially hurts because the counter tech is usually just "okay" against it, and "terrible" in any other matchup. Ice Block should be reworked completely in its functionality imo, but I suspect they'd never do it. Your opponent having 2 free turns essentially doesn't really seem like a good game mechanic, not really fair to any other class (who tend to die when they'd be reduced to 0 HP).
But again, a lot of people play Mage, and have been playing Mage since when Ice Block was in Standard. I'm sure it'd make plenty people angry. Understandable salt thread OP. You're at least very forthcoming - though wishing death on somebody for playing a card game a certain way is a bit silly.