Well boys & girls; b318isp really told me didn't he?
Sorry mate, but I found your post to be a little on the harsh side so I think it only fair that I respond in order to ask for some clarification and clear up a couple of points.
1/ If the vehicle weight doesn't change, how can the sidewalls of the tyres carry proportionally more weight?
2/ Wider tyres will give you a bigger contact patch. It may not be a huge difference but it's a physical fact none the less, otherwise what's the point in fitting them and has the motor racing fraternity got it so wrong for all these years?.
3/ I believe you may have misread the formula that you quoted. I think the one you are thinking of is Pressure = Force over Area (at least that's the one shown to me in the SI Units book for Mechanical Engineers).
Using that formula, where: P = the pressure exerted by the tyre upon the ground at any point within the footprint of the tyre, F = weight of the vehicle and A = the footprint or contact patch upon the ground.
Assume for this exercise that a tyre has a footprint of 100mm along the longitudinal axis of the vehicle and that footprint areas are perfectly rectangular (I know they are not, but it's easier to show the calculation in this example than an eliptical shape). Assume also that the vehicle is perfectly balanced, with an even weight distribution of 700lbs at each of the four wheels (total 2800lbs).
With a 195 tyre, the equation would read, P = 700 (195 x 100)
Convert the metric units to imperial and P = 700 (7.677 x 3.937)
P = 700 30.224 sq ins therefore P = 23.160 lbs/sq in
With a 205 tyre, the equation would read, P = 700 (205 x 100)
Convert the metric units to imperial and P = 700 (8.071 x 3.937)
P = 700 31.775 sq ins therefore P = 22.029 lbs/sq in
The bigger the contact area, the lower the pressure on the ground. Fact.
4/ Racing tyres are not designed to run at much lower pressures than car tyres. The pressure is dependant on many variables (type of surface, track temp, air temp, track shape, driving style, atmospheric pressure, moisture content of the nitrogen used to inflate them, etc, etc) and these pressures can be anywhere between 15 and 40psi.
I mentioned racing merely to illustrate that people with a much greater understanding of how tyres work, agreed with my theory! It was not meant to be taken as a literal comparison.
I'm not trying to belittle you here mate, because you do have a valid point to make. Let's keep it friendly, eh?