Phoenix Dive should stay a warrior skill book. It gives warriors ways to get in close for melee, and gives them a short counter to ranger and mage fire surfaces. Warriors have few interesting skill books as is (though I consider them all very effective), and pyro already has plenty.
I disagree with the idea of limiting the range of escape skills. Combat gets incredibly hectic as it is already, and closing gaps isn't that big an issue anyway. I've had multiple instances in dos2 where a character in a far off distance walked up to me and had enough ap to stab me in the back 3-4 times killing a character.
It's one or the other: melee guys only need Phoenix dive because everyone else gets long range escapes.
If all escapes get shorter range, it becomes much more reasonable for a warrior to run the distance(The Pawn helps with that too, and you will take it just to reposition for those 0.1m away attacks), and as I've mentioned in the Whirlwind suggestion, it's a much more interesting way to counter mage surfaces by strategically removing them, than it is to gain immunity to them, especially one specific type of them, and an immunity that's there for a completely different reason.
I really liked the idea of saving up on ap by smart use of movement skills like battering ram to move 15 meters where otherwise id use all my ap, and leave myself vulnerable if i walked the full distance. Its a system I loved in DOS 1 and i'm, glad its still here. I'd be alright with the idea of lengthening the cool downs by 1 or 2 turns though.
Closer to doesn't mean exactly equal, and it is a problem when you can cover 4 times the distance on some of those moves. In that regard, Battering Ram is already okay, Tactical Retreat is absolutely not.
I feel like you guys are focusing too much on ap cost rather then cool down duration, which I feel has a much larger impact on the flow of a battle. Rather than increase teleport's ap cost to 2, it should have a cooldown time of 5 turns, so that you are more wary of when you use it rather than just using whenever.
AP cost is the more interesting choice to make when using an ability. If everything was gated by just cooldown, you'd end up with what's essentially happening already: people blow their load on an early combo, and then just mop up the field with weapons. 5 or 15 turns of cooldown makes no difference when a battle lasts 4 turns.
Increasing or decreasing the AP costs alters the flow of combat in much more meaningful way, because it alters how much you can do in one turn, rather than how often you can wipe the board.
I disagree that just because mage type characters have the most interesting options rangers should outright benefit the most from height (interesting doesn't translate to best), and I personally feel mages are the overall weakest currently.
In terms of presentation; it makes no sense for most magic to take advantage from the mechanic, because the way it's cast makes it appear to always have it, or makes it irrelevant.
In terms of gameplay mechanics: I will repeat that everything that can be used to differentiate Mages from Rangers and Fighters(etc.), should be fully taken advantage of.
Giving each class a unique relation with the height-advantage is infinitely better than having all of them treat it equally.
