Sorry, I should have said wheel rim damage: the low profile tyres fitted to the larger diameter wheels make the rims more vulnerable to kerbing. This is normally only a problem if you are a bit of a careless parker.
Another downside is the tendency to 'tramline', that is for the steered wheels to follow any change in the road surface, including painted white lines. This can be disconcerting. The effect, I think, varies with particular tyres.
Also, the cost of tyres may be quite a bit higher. Not being very encouraging, am I?