Played with an xbox controller. I'll try to focus specifically on the controls on this commentary.
Took a while to get used to it but after that I was swooshing all over the place, doing complex maneuvers mid-air etc. I'd say it works, but that's not saying much. Good or bad really depends on what you are trying to achieve. For example, Flashback, another world and prince of persia (the old one) are all very restricted, the player is stuck to a grid. That doesn't mean it's bad, it serves its purpose. These games would break if the movements were fluid and free.
So, yeah, what are you trying to do? I noticed the attack button mid-air makes the character stand still in air for a short time, that is common in hack'n slash kind of games, where you can perform combos while jumping etc.
I'm trying to do 'fluid' and controlled movement -- like 'modern' Prince of Persia (Sands of Time). Or more like Muramasa. Or Kung-Fu Rabbit (I've actually written player-movement after playing it -- to test if some problems can be solved).
I'm not restricting player to the grid (hate grids) -- game world can be pretty arbitrary geometry actually (movement restricted to XY-plane). There are restrictions on where you can grab the wall. And of course you can't go higher that double-jump and farther than double-dash in air.
Attack does stop vertical movement, that's intended behavior; it's just no restrictions on max consecutive air attacks, yet. I've planned parts of levels where you should do things like 'jump up, destroy obstacle, air-dash forward' -- falling down during attack will be annoying in than scenario.
I'm still not decided how much combat need to be the game -- original idea was that game more about exploration/acrobatics than combat. Currently you can't actually kill enemies at all, only avoid being killed by them.