Yeah, it would.
Going to 205/40/17s on standard Avus wheels will sort out the sidewall movement.
But fashion dictates people want wide tyres...which sadly kills feel.
The wider the tyre, the more the grip, fair enough..but the car becomes blunt, with no warning of grip running out and the steering gets more numb.
I once tried a set of 7" x 16" BBS RX with 215/40/16 tyres on my S3..and apart from lightening acceleration from the much smaller rilling radius, the steering improved due to lesser width and less gyroscope effect and the car just felt more alive.
I would like to have tried an S3 on 205 or even 215 tyres...just to see.
Going wider, was in my view, the last thing the S3 needs.
It has plenty of grip on 225s - so much you can cook the clutch - so why not go narrower and give the chassis some feel and a bit of movement?