I've been riding a bike as a racer, tourist, and athletic recreational rider for 30 years, and the only times my tires have actually slipped around turns have been on gravel, water, road paint, manhole covers, or oil. The crashes have always been caused by bad luck, bad planning, or bad technique, and I'm skeptical how much difference a softer rubber would have made. On gravel, oil, paint, and manhole covers, surely none. Maybe on a wet road, but even then, I'm skeptical. When it's wet out, that's no time to set another PR for lean angle.
Dry surfaces are another story.
I've read lean angle charts comparing different brands and rubber compounds, but I've yet to reach the traction limit on a single-compound tire while leaning into a turn, and I've never seen or heard of anybody doing that.