Well, some teams have pretty much done that in the past though for different reasons. Williams, during the recent decades when they were cash strapped and behind, pretty much adopted a design philosophy centered around low downforce and low drag, since it's much easier to design for that than for sophisticated efficient downforce. This made them worse overall, but with higher peaks on tracks like Monza where you just want low drag. For a bottom team, it's better to be 19-20 every race apart from say 3 where you have a chance to be 10th, than it is to be consistently 15-16.

Sacrificing performance for less turbulence sensitivity is sort of self defeating though, as while you might now be able to follow closer you're giving up the performance that allowed you to threaten the overtake in the first place. Or indeed as you say qualy performance will suffer too.