I've had soft wheels before. In 1990 I got a bike with 105 hubs, double butted 15 gauge spokes, Wolber GTX rims. Soft, plush and yes, kinda vague when cornering. Also rubbed brakes a bit when stomping on the pedals out of the saddle. Killed a rim on a pothole in the mid 90s. CXP-22 and new 15 gauge double butted spokes, but same tires and hubs. No more brake rubbing, felt stiff, kinda dead at first but tracked better in hard corners. Definitely a difference.

I reckon there's a happy medium but I'm not gonna go out of my way to chase it.