The roads around here aren't really grooved. We don't have that much in the way of heavy vehicles. Some of the trunk roads can be bad though.
As you say, most people never get near the limit of adhesion on corners. If the tyres are not squealing you are no where near the limit. I did a racing driver's course at Knockhill Race Track, near here, and it is quite something the speed you can get through corners. Even on the bog standard SEAT Leon Cupra they start you off on.
What I find with my Jazz is that, in the wet, it starts to understeer very quickly. And that is without elevated tyre pressures. I think the Firestone Multihawk 2 tyres, on the front, are just rubbish. Tons of tread but no wet grip.
I love pushing a car on a bend. There is a part on the nearby M90 that turns through 270° and there is always someone who wants to overtake as you turn into it. They then have to do about 20 mph more than I do just to get past. And I just nail it round there. Unless it is a four wheel drive Audi or the like, they have no chance.
And me at Knockhill.