It feels very disorientating to me.
I find trying to do anything but the most basic movement to be too difficult. For instance trying to walk through the gap between two tiles while changing which way the player faces ends up being too confusing and messy. That task I can easily achieve in a first person game, or in a top-down game with a more traditional control scheme of WASD mapping to fixed directions irrespective of player rotation.
From a first person perspective which direction in the world the WASD keys map to is information given directly to the player from their view. Here the player needs to perform an additional cognitive task to transform the WASD map based on the player character's current rotation.
It's quite possible to still navigate through the world with this control system, but I find myself relying far more on constantly holding a particular direction rather than smoothly alternating between keys. I'm left with the feeling that I could be moving about far more easily if WASD mapped to fixed directions. Interestingly there's no actual restraints placed on the player's movement by your control scheme (for instance, you can still back away from an enemy while shooting) it's just that to perform the movements requires more mental work from the player.
Yeah you make a good point. I actually didn't like relative controls before either..but I feel like for a certain type of gameplay, namely slower-paced navigation, it feels cool to me. The movement lines you get are smoother and curvier. So maybe with Geometry Wars this would be terrible, but a slower-paced metroid vania type game this could work.