Strafing is and has been a staple of FPS gameplay for some time and it's strength is amplified on a console shooter due to the natural imprecision of the control pad as a method for control in an FPS. Dust further reinforces movement as it's primary defense for various reasons.

I'm far more concerned with the bunny hoppers who can jump anything up to 2-3 stories high than I am with strafing. The use of cover is dangerous in this game as you can be one-shotted with a great deal of ease even when pretty well tanked and warbarge strikes further compound issues with cover (barring snipers and other distance campers obviously) so that movement is just the best defense you can have. Part of that is the "wiggle dance" you seem to hate.

People do so much damage that even in cover, any angle you can be shot at will kill you, with the general ineffectiveness of the radar (to encourage scanning, a very clever mechanic), no cover is truly safe as it would be in a more traditional FPS like one of the Halo Series for example. All of this pushes down the trend towards cover and tactical movement and pushes up the use of strafing and semi-randomised movement in the game. Combine this with remote explosives and mass drivers and other large splash damage weapons and cover is a very dangerous place to be, not inherently, but just because standing in one place is generally suicide.

If you want to push it back the other way then you need to do more than just nerf movement, cover has to be reasonable and safer than it currently is. I have no idea how you would implement it, but I would buff cover so that if you're shot when you're in cover you get a form of damage resistance/hardening to your shields/armour. Cover dampens damage that comes from the side you are in cover or something similar to that. Off the top of my head I can't think of a reasonable way to implement this but I'm sure people here would have other ideas for buffing cover.