This simply is not true. Case in point; take a 2004 Ferrari F2004:
- 1.8m wide
- 324mm wide contact patch (380mm - 4 x 14mm, from the grooves, that's equal to the pre 2017 contact patch with).
- Blistering fast (records only recently broken by the 2017 gen. cars).
So the car nor tire does need to be that wide to be fast. The reason the pre 2017 cars look funny like in your picture is because the high and narrow rear wing. If you look at a F2004 rear shot it looks fine,. Why, because there is a normal rear wing on it:
I agree the wider cars and tires look even better, but to me that absolutely does not weigh up to the disadvantages listed in the opening post.
If you compare the available track width between a 1.8m car and a 2.15m one you loose 70cm of track width in the side to side situations we so desperately want to see more of. If that does not sound like a lot, imagine the apex coming in 70cm and what that does to the ability to take a tighter corner with to cars side by side.
Compared to the 2016 season the frontal area of the tires will have grown a massive 34%! Furthermore drivers are already sounding the alarm bells over the visibility with this tire size, not being able to see the kerbs (remember there will be an additional air deflector on the front wheels as well). Something the larger diameter rain tires would only make worse in already challenging visibility conditions in the rain. Imagine not being able to see standing water because a huge tire is in your view.
As you say though, the cars need to be shorter to be in proportion with the 1.8m width.