With some offset combinations and sidewall sizes, 17's do actually look alright.
The pictured Glanza IMO looks brilliant
However, with the wrong design of wheel, and incorrect offset, a decent looking machine can turn into something of collasal shittyness
I was considering some Compo MO's in 17" for my GT, not only to fill the arches a little more, but to get the power down a bit better in the continuous damp which seems to be current in the UK.
As with some of the statements you've made, you're partially correct. The stability of the car will change, but won't nessasarily improve. Wider tyres will tend to cause sideways movement at higher speeds with the width of the tyre being hit by more air.
Bigger cars, which come standard with wider tyres, tend to have small flares infront of the front wheels, to direct the air around the leading edge of the rubber, to combat this issue.