Edit: This post is a reply to a post Jim deleted that suggested that heavier sway bars would create mixed handling. This was a misunderstanding as Jim thought I was talking about sway bar bind, not more anti-sway. My car currently oversteers everywhere, it is not loose and pushy at the same time like this post on its own might suggest.
How in the h3ll do you end up with a car that is both pushy and loose at the same time by making small changes to sway bars?
Changing camber away from optimal or putting toe out in the rear or cranking the air pressure to the moon are examples of "taking away grip".
If I go up 50lbs on the front springs and go up 50lbs on the rear springs, I haven't taken away grip from both ends of the car necessarily, I've just changed the overall spring rate.
Adding stiffer sway bars front and rear is a similar sort of change. On a track that requires more independence in the suspension, it hurts. On a perfectly smooth track where it just reduces body roll, that might help.
Now it could be that our cars prefer less sway bar everywhere due to having good camber curves, but that shouldn't have anything to do with pushy and death loose at the same time.
As long as you're not taking it to the extreme, sway bar changes just help decide which outside tire gives up first. The trick is to balance the outside tires so they give up at the same time after having given their best effort at the best pressure and camber while in good contact with the road (shocks).