You would have to valve a shock differently for a 4 link if you were not running sway bars. I don't think anyone really does that.
4-link kits should come with a larger sway bars, but most kits don't....LOL
The thing that I don't like most about 4-links is typically you do end up with some bump steer and then if you actually wheel the truck the front driveline isn't that happy...at full droop. Seen drivelines and t-cases grenade...LOL
It all can be done correctly but nobody wants to spend the money to do it or I guess really cares that much....LOL. or maybe doesn't even know...
Just because you have king shocks doesn't mean you can take the sway bars off either...LOL. There is like a million ways to valve these things...LOL. That is one of the cool benefits of the bypass/adjustable shocks. Just keep cranking them down. I can make my truck lean or go around a corner like a race car...LOL
Like this truck....16" lift and no sway bars....LOL This one doesn't have bypasses, it is just valved properly....
https://www.youtube.com/watch?v=Jzs0Fl8bRVA