With lower profile tyres, one must shift platform and wheel tyre load control from using tyres like shock absorbers to using properly designed suspension instead of using no travel hacks. The worst example was the shark nose weirdo Williams BMW F-1 cars from a few years ago, with the nose design compromising suspension geometry to such a degree that the wheels don't get camber recovery with bump travel. In fact, camber grew more POSITIVE with compression! Explains all the uber understeer problems drivers complained about, especially as speed climbs and the suspension compresses further. Besides, which would you prefer to control the car, well tuned springs and dampers or the sidewall which has ever changing properties?

So, why is a lower profile (within reason of course) tyre grippier? Lower profiles allow stiffer sidewall contruction, allowing more stable contact patches. More contact patch stability is always good if ultimate grip is the aim. Of course, this would mean that the tyre works at smaller ranges of slip angles, but with F-1 cars as aero dependant as they are today, larger slip angles aren't too productive. Current F-1 wheels are what they are not because they're the ultimate in grip. They're the result of restrictive regulations.

Speaking of which, personally, I would prefer regulations that severely reduce downforce generated via wings BUT allow more freedom to improve tyre mechanical grip. Seriously reduces the aero induced anti-overtaking problems whilst keeping F-1 cars as the ultimate Formula cars both technologically and speed wise.

When the Bridgestone tyre engineers said they'll be undrivable, they meant they could be potentially so sticky that the human body just can't take the g's without help. A 15 inch wheel for current F-1 cars isn't excatly a rim and rubber band setup.