I get the philosophy, but I think there is a bit of tweaking that could be done. From the purely mathematical side, under the system as it stands, I think that 1-2 should be failure, and 3-6 success, for two reasons. The first is that if you're going to do a binary, you might as well use coins as dice. The second is that spell difficulties are a touch overtuned as well. I like the ebb and flow of magic, and how that functions mechanically, but you'll never consistently be able to cast anything reliably over difficulty 3 most of the time, and most of the spells aren't enough better at higher costs as opposed to just casting twice. I get that the intent was to force the players to interact with the Aetheric Influence table, but that has it's own difficulties, and a 33% instead of 50% failure rate would actually probably lead to players making riskier moves more regularly.
On the subject of the Aetheric Influence table, the consequences don't quite work. Only the last hit point matters, and the health damage only takes a wizard down to 12, beyond instant kill range for any of the spells, or even being surrounded by minions. The wizard doesn't seem to have much reason to ever move or hit something with their hands, as even a difficulty 2 spell is going to consistently match their strength, and unless I missed something, spells don't have range limits. The action limit at 11 and the turn skip at 12 actually hurt, but otherwise the actual consequences are mostly academic.
Given the above, and to better lean into the theme, I'd suggest giving the wizards bonuses as they accumulate additional Aetheric Influence, right up until they explode. For example, you could keep the 50-50 success rate, or even lower it to 66-33, and change the Aether Deck to use 2 through 4, with higher levels of Aetheric Influence giving Wizards more Native Aether. This would enable them to cast additional spells, but it also encourages them to dip deeper and deeper into Aetheric Influence. You also should add some form of range limits to the spells, and probably could get away with making the wizard's strength add dice to spell rolls, so you don't have to add a stat. It could also feed into spell range as well. Under this, increasing Aetheric Influence would mostly add strength, and maybe health on alternate rows, right up until it explodes you.