The actual research on this is quite interesting. First of all, a wider tire does increase the contact patch, but only very slightly. Some of this is due to pressure per square inch, but also the stiffness of the sidewall is a factor. What is really interesting is that lowering the air pressure does not increase the contact patch virtually at all within the operating range of the tire. But there is a cooling effect of a wider tire as it remains slightly cooler. Whether that is good or not depends on the tire compounds used. Some compounds have more grip at higher temps and some have more grip at lower temps. We also know that a wider tire will have a negative effect on mpg due to wind resistance.
I was surprised that tire pressure didn't make a big difference, as that is what seems obvious, but it is just not true due to the stiffness of low profile sidewalls. In fact, depending on the tire, lowering the pressure could actually decrease the contact patch as the tire begins to form a concave surface. Overinflating will cause a convex surface also lowering the contact patch. Tires are designed to achieve the maximum contact patch at the recommended tire pressures.
If we keep the same 45 profile on the tire and bump up the width, we also have a taller tire. While that will make the speedometer record a 1% slower speed, it doesn't affect the contact patch much. However, the taller tire will give slightly higher mpg, slightly reduced performance, and given that the sidewall is slightly taller, will give an incrementally better ride.
These results would argue for keeping the current width of the tire for a good balance of performance and mpg. Changing to 225 might make you feel better, but it will have a very minimal affect and is not worth the effort.
From what I can take from all of the articles that I've read, and as you claimed in your final statement, the quality of the tire has the greatest impact on overall performance. If you want to move to 225's, it might increase mpg and decrease performance very slightly, but you're not going to really notice much of a change.
There will be some here that will talk about new wider wheels and much wider tires with a lower profile. Before I studied this subject, I always thought that would provide significantly better traction but significantly lower mpg. But I've learned that the contact patch doesn't change much. However, the lower profile with a stiffer sidewall, while giving a poorer ride, will give better lateral traction. So if you are racing your car and do a lot of cornering, it will make a difference because you will have more rubber giving lateral contact. Also, the compounds used on very wide tires are softer than the compounds on skinnier tires thereby increasing the grip.
When I replace my current Dunlops, I'll probably move to 225/45's just to accentuate the mpg very slightly as I seem to have enough power with the 2.5L. But the most important factor is the quality of the tire for my specific needs. You should never skimp on tires or brakes if you want to get the most out of driving.
